Yes, it is possible for a region to have more than one Multiple Listing Service (MLS). This is the case in New York City.
There are no less than four separate broker databases in NYC: REBNY RLS, the OneKey MLS, the Brooklyn MLS and the Staten Island MLS.
While the REBNY RLS has the largest overall footprint in NYC, other databases outperform in certain areas of the city. For example, the Brooklyn MLS has a strong presence in South Brooklyn but the REBNY RLS dominates in Brooklyn neighborhoods closer to Manhattan.