A modular connector assembly for a medical container may include a plurality of covers and a plurality of adapters. Each cover is connectable to a cooperatively dimensioned medical container. Each adapter is attachable in fluid sealing engagement with each cover by an interface assembly including a first interface segment formed on each of said plurality of covers and a second interface segment formed on each of said plurality of adapters. The first and second interface segments and corresponding ones of the covers and adapters are initially separable and subsequently connected to define a fluid sealing engagement between connected ones of the cover and adapter. The structural configuration of each of the plurality of adapters is variable to define a different one of a plurality of medical connector types.