multiple vendors on one award??

Good afternoon, Looking for some knowledge and input. The situation I have is regarding arbitration services. In the VA, used to be able to pay for these services with a 1358, the facilities cannot anymore. When these services are required, it is not as simple as picking who will provide the services, the union and the facility has a pool of arbitrators that they can select from, but they both select about three, then agree to one. So anticipating who will provide the services is not allowable until almost crunch time. When 1358s were allowed to be used, those arbitrators did not have to be in SAM, so another problem with a contract moving forward. Is there some sort of BPA or other contract vehicle that would allow for multiple vendors rather than a BPA for all of the potential arbitrators? obviously, there is no competing among the BPAs or whatever is in place because it has to be mutually agreed to. Obviously, looking for the simplest method to be able to provide the facility and union arbitrators when required. Thank you