Once a pilot is type-rated in an aircraft, (s)he is type-rated in that aircraft forever. For example, if a person flew as captain of a Beechjet prior to working for an airline, then as captain in 727, 737, and 777 during his airline career, then his pilot certificate would retain all of those type-ratings. In order for each rating to remain current, however, the pilot must have type-specific recurrent training in the type every year. I believe that a pilot who is typed in 2 different airplanes can do trining on each type every other year, but I'm not sure how that applies to pilots with more than 2 type ratings. The simple answer to the question is that, yes, a pilot can be type-rated in more than one aircraft at a time. Airlines, however, do not generally have pilots fly more than one aircraft type at any point in their careers.
As purdue said, there is nothing preventing certification and currency on multiple types (at least not in the US, cant speak for the rest of the world). I have known a FEW pilots, usually management or instructor pilots who are "cross trained" on two types, but this was at smaller regional airlines. Most airline union contracts forbid the practice for line pilots. So even though you may transition from say 737 First Officer to 767 FO, and for a period of time be perfectly legal to serve on both aircraft, it is not allowed by company work rules. This is mainly safety driven. Most commercial airplanes have emergency checklists containing "memory items" for the worst situations, such as engine fire or failure. If you were flying two types regularly this could produce a hazardous situation if you have an engine come apart and cant remember which memory items to accomplish.
It is much better to know one type like the back of your hand than try to juggle two.