In the countries using FAA rules (or with rules inspired by FAA), you could hold many type ratings current. However, read FAR 61.55 and FAR 61.58, which applies to non-airline flying.
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When I was with PanAm, we could be qualified/current on
two types and I was qualified on 707 and 727. I had to do an annual proficiency check on each type flown, and a 6-months instrument proficiency check on
one of the types I flew as PIC. In practice, that meant a simulator check on one of the types, and the next simulator check was in the other type. American Airlines and TWA did same in these days. As F/O, you could do same with 12/24 months recurrent simulator checks.
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Clay Lacy (retired UAL captain) holds some 50 type ratings, obviously not all of them are current for part 91 flying. He reportedly has logged some 45,000 hours. I know he is current on all Lear types, all Gulfstreams II through V, on the 727, 737 and DC3... His buddy John Lear (son of Bill Lear of Learjet fame) also holds some 50 type ratings and licences valid for fixed wing, helicopter, gyroplanes, blimp, hot air balloon, instructor, flight engineer and navigator (what did I forget...)
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Funny thing about Clay Lacy... One day he got a HS-125 rating... The FAA inspector, was busy filling the "paperwork" for the new rating asked him "how many hours on the this HS-125 type...?" - He answered... "just about 60 minutes, the flight I did with you today...!" -
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Here in Argentina, I am current as 747-200 PIC and check captain, but also qualified as F/E on type... I also occasionally fly a Lear 31A with the CEO and other upper level airline managers...
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Since I am now senile and near retirement, I am happy to remember that my old 747s have 4 engines and that the flight deck is upstairs... not easy to get up there on my wheelchair pushed by these sexy flight attendants. Where do I stow my white cane is none of your business... and my hearing aid is wired to essential power bus...
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Happy contrails