If you decide to paint over existing bottom paint and not remove all the paint layers first, make sure your new bottom paint is compatible with the old. For example, you can't apply vinyl bottom paint over non-vinyl bottom paint because vinyl paint contains powerful solvents that will cause non-vinyl coatings to detach.
Most bottom paint manufacturers have their own brand-specific bottom paint compatibility chart. Below are a few compatibility charts from Interlux, Sea Hawk, Pettit, and TotalBoat, for example.
INTERLUX
SEA HAWK
PETTIT
TOTALBOAT