The best I can come up with are Liquid Democracy (Liquid Delegation) or what I term Liquid Representation which would allocate each eligible voting citizen a single vote. In Liquid Democracy/Delegation, each citizen can either vote on an issue or vote on a delegate to vote on an issue. Let's say the issue is related to climate change. If you would feel uncomfortable about your information ability to make an informed choice, you can instead choose to delegate your vote to someone else more informed, say Bill Nye the science guy. If Bill chooses to vote on an issue, his vote now has the power of 2 votes (his and yours, assuming no one else give Bill a voting power). However, if Bill does not feel he is competent enough, he can transfer his vote to Neil de Gras Tyson, who will now have 3 votes (his own, Bills, and yours, assuming no more votes are given to Neil.).
In this system, Neil does not have a term limit on your vote on this issue. If you disagree with Neil, you can pull your vote from him and give it to someone else.
Liquid Representation is similar, but uses a Representative system for the purposes of creating possible laws to this question.
In this example, you would still vote on your local region's upper and lower houses (Two Senators, one Representative if in U.S.) however, if at any time, you disagree with your representative on an issue (say you love his environmental policies, but don't agree with his gun control stance) you can move your vote to another representative from another region. The main difference to Liquid delegation is it still limits who can create laws, but will empower their votes for that law based on public support. Thus, your representative may not have uniform voting power between all issues, having strengths in some regions and weaknesses in others. This also has the benefit of a default vote on an issue (if you are apethetic, your vote defaults to your local representation. You must actively move it for a bill or issue. This allows you to have some say in an issue you really care about, without requiring you to read every single bill before a representative. The assumption here is that if you don't care one way or the other, your most local official will know what you want. It also requires fewer changes to a very difficult to change constitution to implement.
The problem with these systems is that most assume a sort of "Social Network" function is in place so you can just pull out your phone and change your stance, which creates all sorts of cyber crime opportunities as well as possibly disenfranchises citizens who have difficulties in getting Internet connections (you would need to implement a non-partisan method of getting connectivity to those who do not have it.). It also creates issues with Luddite citizenry such as the Amish, who on matters of religion do not use certain technologies, including cell phones and the internet, so an alternate way of re-deligation would need to be established for them (perhaps a service that will hold their votes in a way that can be trusted to vote in their interests).
A quick discussion on Direct Democracy and Referendum Voting. Direct Democracy can be used in tandem with Representative democracy with little issue. The two best countries to see this are Switzerland, which has referendum voting at the Federal Level and The United States, which has some system of referendum voting at the state level (The most common being referral voting, where the legislature can opt to pass a law by citizen vote, which is available in all 50 states. Delaware is the only state that doesn't offer this option for the state constitution. 24 states have some form of citizen initiated veto on laws, and 19 have citizen initiated law proposals, 21 have citizen initiated constitution amendment processes).
Swiss Direct Democracy exists on the Federal Level (with some slight changes in the nature of the executive branch, is pretty much the same as the United States federal system.). Here, citizen Democracy is a futher check and balance on government and is itself checked by other branches of government. Swiss citizens can create or repeal a law by getting 50,000 signatures from any Swiss citizen across any of the cantons (similar to States in the US; At the Canton and local level of government, these numbers will be smaller.). For constitutional amendments, this number is doubled. If a petition achieves this threshold, it will be placed on the next election's ballot. To pass, it must achieve simple majority for all canton and lower levels. At the Federal level, double majority is needed. This requires a simple majority of both the general population of Swiss citizens AND a majority of Cantons to favor the proposal. (For a U.S. perspective, this would be similar to a rule that the President must get both the electoral college vote and the popular vote, rather than just the electoral college). The Swiss hold elections four times a year because of this, which does create some voter appethy at times. Compared to the United States, which votes once every two years not counting special elections.
Historically, Athens is the most famous direct democracy, though they had no sufferage. The 1871 Paris Commune was decentralized direct democracy and everything was up for a vote. Again, women sufferage was not established, though women were highly involved in campaigning. It fell apart in less than year due to lack of infrastructure needed to facilitate voting.
New to the scene is Rojava (officially known as the Democratic Federation of Norther Syria) which is an unrecognized state, which declared autonomous status in late 2012 and federated in March of 2016. They seem to follow a model similar to the Swiss, but include neighborhood level governments. Uniquely, they have co-executives at every level, one male, one female. At this time, it is quite early in their history to make remarks, and its still disputed if they will be a new nation, or a successor state to Syria writ large.