For buyout assignments, as far as I know, you can request as many at one time as you want. You have to finish all of the reviews for them before you can request more, however.
For free assignments you are allowed one a month in your price range. If you are in the description review program you get assigned products when your turn comes around, I have had up to three assigned to me at one time.
If you are in the video review program you also get one free toy a month in your price range.