Yes, units located at the same site can be accredited by different accreditation bodies (dual accreditation). Some of the downsides to dual accreditation include the increased cost and paperwork associated with dealing with two accreditation bodies and having to undergo two MQSA inspections (because each separately accredited unit would be considered a different MQSA certified facility).
While there are downsides related to dual accreditation, there is at least one situation where a group might decide to have its units dual accredited. For example, suppose a facility already has a film-screen unit accredited by a State accreditation body. The facility then purchases an FFDM unit but the only body that accredits that unit is the ACR. The facility has two options. It can either drop its State accreditation and have both units accredited by ACR (both units are now part of one MQSA certified facility) or proceed with dual accreditation and keep its film-screen unit accredited by the State and have its FFDM unit accredited by the ACR (each unit is now its own MQSA certified facility). In the case of this dual accreditation, FDA would allow these two facilities to be grouped for MQSA inspection billing purposes to reduce the cost.