No, there are no limits, simple as that.
Countries typically don't want more refugees than they absolutely have to accept (and, in spite of what you might have heard, that very much include Germany) but there is nothing preventing them from providing protection to anybody who meets the definition if they want to.
Case in point: You might have heard of the Dublin system. In spite of widespread confusion, it creates no obligation for refugees to formally seek asylum in one place rather than another and absolutely no obligation for a country to decline to process an application. What it does is offer a way for a country to get rid of an application (and force another country to take care of it). But it's always optional, each and every EU country legally retains the right to examine any application. In the case of the Dublin III regulation, that's even spelled out explicitly in article 17(1).
In fact, any quantitative limit is almost surely illegal, under international and EU law. You either meet or do not meet the definition. If you are the 1000000th person to enter the country during a year and you meet all the conditions to be considered a refugee and all the procedural requirements to see your application processed in that place, you are as much entitled to international protection as the first person who showed up.
Or said otherwise: You can be as restrictive as you want, take an absurd interpretation of the rules and effectively reject all applications (as Greece has been doing at some point) but not announce in advance that there will be a specific number you are prepared to accept.