OP is right. You can get qualified on multiple aircraft types, but to maintain currency is a different topic altogether. In the US for example, at least for private pilots, you need at least 3 take offs and landings in the last 90 days in the aircraft (category/class/type-rating) to be able to carry passengers. Then there's extra requirements for night currency and instrument rating currency.

I would imagine the airlines have even tougher currency requirements. That said, it's probably possible to maintain currency in several aircraft types depending on the frequency and how the jobs are scheduled.