I'm interested in works of political theory, not the actual policies
or practices or the thoughts of think tanks or other organizations.
Despite this, since I'm familiar with actual current and historical practice, I'll speak to that. In part, because your question is sufficiently vague that it is hard to know what you really mean and some examples could clarify the kinds of things you are thinking about. For example, I'm not sure if this 1999 book is close to the concepts you are thinking about or far afield from them, it states in its abstract:
This book . . . seeks to explore the implications of conceptualising
citizenship as something which is not necessarily tied to a bounded
political community. The reasons why this has become a focus for
political theoretical argument in the recent past are varied. Many of
them are referred to in Heater’s own consideration of contemporary
cosmopolitan ideas in his book World Citizenship and Government
(1996). The reasons range from the consequences of perceived processes
of globalisation and increased economic and cultural interdependence
and commonality across the world, to the growing significance of
global ecological issues, to the growth of such trans-state political
structures as the EU. In relation to this book, however, the most
important impetus for argument about the concept of cosmopolitan
citizenship stems from normative ethical and political concerns about
the possible costs and benefits to political order, community, rights
and participation of opting either for a cosmopolitan or a bounded
citizenship ideal. This is the argument which is set out in the
following two chapters by Linklater and Miller respectively, and
around which the rest of the contributions to this book are
Whereas the role of the individual qua world citizen has hitherto been
a weak and intermittent strand in Western cosmopolitan political
thought, recent concentrated interest in both the theory of democracy
and citizenship in the context of the state is starting to spill over
to the global plane. (Heater, 1996, p. 209)
It is hard to tell.
Are there political theories which support a broadened view of
citizenship? Examples could extend citizenship to businesses,
religious organizations, or other voluntary associations.
One of the core political theories of this type is "nationalism" in which one or more populations, often with an ethnic or religious foundation, within a state develop a sense of community and identity that corresponds to citizenship, more or less, rather than arbitrary politically drawn boundaries.
For example, consider the concept of Ummah in Islamic political thought:
Ummah (Arabic: أمة) is an Arabic word meaning "community". It is
distinguished from Sha'b (Arabic: شعب) which means a nation with
common ancestry or geography. Thus, it can be said to be a
supra-national community with a common history.
It is a synonym for ummat al-Islamiyah (Arabic: الأمة الإسلامية) (the
Islamic Community), and it is commonly used to mean the collective
community of Islamic peoples. In the Quran the ummah typically refers
to a single group that shares common religious beliefs, specifically
those that are the objects of a divine plan of salvation.1 In the
context of Pan-Islamism and politics, the word Ummah can be used to
mean the concept of a Commonwealth of the Believers (أمة المؤمنين
Another kind of community common in the Middle East, although the connotations get muddled in translation, is the notion of a "tribe". For example, about three-quarters of the people of Iraq are affiliated with one of its 150 tribes and loyalty to one's tribe can often be stronger than loyalty to a corrupt and repressive government that empowers your enemies, whose boundaries and formative foundations are largely a product of a post-World War I effort by colonial powers to manage the collapsing Ottoman Empire as they saw fit.
Of course, in the U.S. there are true semi-sovereign tribes of Native Americans with genuine citizenship concepts under the umbrella of the federal government. Another group of people who operate as a semi-sovereign society in the shadow of national governments of the European Romani people (a.k.a. Gypsies).
Historically, weak state institutions have led not to the idealized world of anarchists and libertarians, but instead to extended family tribal-like institutions and clannishness that subordinate members desire to express individual choice and freedom in the absence of a strong state, to clan needs for mutual protection and more. Clan institutions also undermine national states with corruption. Weak states and the strong clans that arose to fill the vacuum created by weak states were notable in the Scottish borderlands and were brought with Scotch-Irish migrants to places in the U.S. like Appalachia as epitomized in the long clan on clan blood feud between the Hatfields and the McCoys.
In India, the caste system is a center of identity at least as important (and longer lived) than the national government, in which your kinship and community ties to members of your jati a hundred miles away may be stronger and more relevant than your ties to people half a mile down the road. A jati is a mix of an extended family at something like a tribal scale that is strongly endogamous and membership in a hereditary professional guild.
A somewhat similar institution to a jati or an Iraqi tribe (something similar but not quite as kinship based also existed in the Roman Empire and was called a tribe), is a mutual benefit or fraternal society, perhaps most notably in the cosmopolitan bonds of the Freemasons.
Mutual benefit societies have been particularly important in immigrant communities in the United States at times when the governmental social safety net was weak. Among the most notable were the Chinese Tongs, especially in the Western United States, which, like the "political machines" of Catholic immigrants in the Northeast, often veered into corruption and gang-like activities (which a gang also being a sort of political identity and citizenship). Political machines and mutual benefit societies, in common with the political parties of the West Bank and Gaza, and in contrast to most modern political parties in the developed world, were notable for actually directly providing services to their members rather than exclusively seeking to control governmental institutions through which services are provided.
For example, these kinds of benefit societies/political institutions (and to some extent labor unions as well) might help you find work and help with basic needs when you are unemployed, might publish its own newspaper (prior to the Progressive era in the U.S., many newspapers were expressly partisan), and might directly intervene to help you with neighborhood problems without resort to governmental institutions.
Similarly, while labor unions organized by employer resemble modern political parties that simply try to influence the employer's actions in favor of workers, in industries where unions are organized by industry (e.g. acting), unions often provide health insurance, retirement plans, and leads in finding work to their members, more like a guild than an employer specific political party for workers.
The Prussian business model, which survives today perhaps most strongly in the economic organization of Japan, puts an employer in a neo-feudal role, providing far more than a paycheck in exchange for work to employees, and instead built around a concept of mutual long term loyalty between employer and employees and their families. The divide between work, play and state in this model is a thin one, for example, with the notorious Prussian Civil Code dictating matters like which day a household should do its laundry. Japan today has one of the smallest governmental sectors in the developed world, because a lot of the tasks of the welfare state, from providing economic support during business downturns to building affordable housing for low wage workers, were assumed by large private employers. Prussian efforts to integrate worker's larger lives democratically into the workplace with employer sponsored institutions was the source of the codetermination concept that puts worker representatives on the board of directors (as a minority) of larger businesses in Germany today.
In U.S. history, the two most notable efforts to develop religious communities that served much of the role of the welfare state to its members that most developed countries provided through government to its citizens, have been the Roman Catholic Church, which has developed a large parallel education and health care system, and the Church of the Latter Day Saints, which uses tithes to finance a wide variety of services and economic supports for members of the Mormon community. Zionism is another such movement.
Another important aspect of religion as a form of citizenship is that quite a few countries, for example, India and Israel, apply different regimes of family law and inheritance to their citizens based upon their religious affiliations. Thus, for example, the divorce laws that apply in India to a Muslim couple are different than the divorce laws that apply in India to a Hindu couple or a Roman Catholic couple. The same would be true of inheritance laws as well, although there are, of course, many kinds of laws to which religion does not speak or for which having multiple rules for different groups of people just would not work (e.g. motor vehicle traffic laws).
A fairly recent academic treatment of the topic can be found in the 2017 book, The Origins of Democracy in Tribes, City-States and Nation-States by Ronald M. Glassman.
Another idea might be called "un-nationalism" and is discussed in this 2015 article whose abstract begins:
This paper seeks to make a moral argument for citizens’ need to create
networks of solidarity with non-citizens. Instead of concentrating on
the political mobilization of migrants themselves, it thus highlights
the theoretical grounds on which notions of responsibility and
solidarity can be extended to ‘non-members’ within established
political communities. This goes against prevalent modes of
argumentation in modern political thought, where solidarity and
responsibility are mostly defined in terms of shared social or
political identities. To establish this alternative line of
argumentation, the paper draws on the works of Emmanuel Levinas,
Judith Butler and Jacques Derrida.
In general, a lot of the notions of allegiances other than to a national government are rolled into the concept of "civil society' as a such of thought in political theory. A related movement within political theory is Communitarianism and the emphasis on the social capital that communities with strong senses of membership develop. Communitarian ideologies often illuminate the political stances of Christian Democratic parties, which are the most common type of center-right party in Europe and have a very different ideological foundation than the right leaning Republican party of the United States, because, while this ideology can be socially conservative it also puts the collectively responsibility to care for everyone and not simply to let people sink or swim at the top of its agenda.
Another exponent of civil society is the notion of cooperative enterprises, one of the most impressive of which is the complex of Mondragon cooperatives in Spain.
Similar ideas were behind the creation of many rural cooperatives in the United States during the Great Depression for everything from electrical and telephone services, to marketing crops, to purchasing farm supplies. There was a political theory behind it dating back to the early days of the Republic, if not precisely a citizenship based one (although it did involve democratic ideals) as explained here:
Building on trade and social guild traditions, mutual aid and
"friendly society" organizations sprang up to address the conditions
of the times, and contributed to the development of the cooperative
business ideas. Arguments that provided a broader rationale for
cooperative organizations were articulated by Robert Owen (1771-1858)
and Charles Fourier (1772-1837), who were inspired by conditions of
the period to search for paths to a more harmonious, utopian society.
The more pragmatic William King (1786-1865) advocated the development
of consumer cooperatives to address working class issues, and his
self-published magazine, "The Cooperator", provided information on
cooperative practice as well as theory. King emphasized starting small
cooperatives with capital that could be supplied by its members. He
stressed the use of democratic principles of governance, and the
education of the public about cooperatives.
One way of parsing out parts of a state that must be handled on a large, geographical control basis v. those which can be organized differently, is to distinguish between the idea of a commonwealth which emphasizes the role of taxing and spending as a governmental function versus the regulatory state that monopolizes the use of force and more generally tells people way they can and cannot do under the law. From a budget and employment perspective, may people are surprised as how large the commonwealth functions of government are relative to the regulatory state functions.