There are no rules about how many papers you can review at any one time or how many journals they come from. You are right it is a great learning experience, but it's also important to set boundaries to ensure that you can conduct quality reviews, both in terms of your expertise but also your time. There will come a time when you have 'too many', and learning to say 'no' when necessary is a good habit to get into.
Dear Joseph, I had peer reviewed a manuscript and I found it interesting but demanding. It requests your effort, hard work and a fortune of your time. Specially, if you have to go for repeated rounds of the same manuscript it is hard work. But, I loved it and it added to my professional experience. Plan carefully before accepting the offers from multiple journals.
I would like to believe so. Each journal is independent, and reviewing one journal has no effect of the other, as long as one allocates enough time for each.
Peer reviewing demands many hours of thinking and rethinking and this is important to enhance the quality of the manuscript. For those reviewers who have time, why not be a reviewer of multiple journals. It improves your reviewing skills and keeps you updated.
I've never heard of a journal that limits what other journals you can review for.
The problem is that it takes time. Sometimes a lot of time.
While institutions give lip service to encouraging this kind of "service," no one gets ahead for doing many reviews. And because reviewers are supposed to be anonymous, it's hard to build a larger reputation this way.
So, the incentives for reviewing many articles are quite low.
Speaking from personal experience, I am a reviewer for multiple journals and it has never been a problem for one (journal) that I am also associated with another (journal).
But, as Dr Alexander Hoffman says, the incentives are often quite low. This sounds terrible but I now selectively review for the "good" ones only because I just do not have enough tine if I accept all invitations.
It depends upon the availability and time devoted for review by the reviewer. In my case I have to limit the journals that I review so that I can focus on it. Quality review output is important than quantity.
As a scholar-to-be, I am volunteering as a reviewer in four peer-review journals. At first, it was fine, since each of those has different pace of paper circulation and it was quite manageable. However, as time goes on, it became demanding. Then, I tried to narrow my focus of interest and went working with only two journals that were strongly related to my interest. For me, it is the best practice! And the learning curve from all those experiences is quite satisfying for me.