Is there a way to award a sole source to the NPO we are currently using or do we need to go through Source America?
If your service is on the Procurement List, then you must use the AbilityOne participating non-profit agency if they are available within the period required. See FAR 8.703 and 8.704. "No other provision of the FAR shall be construed as permitting an exception tot he mandatory purchase of items on the Procurement List" (FAR 8.704(b)).
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FAR 8.706 has purchase exceptions. Exceptions have to be specifically authorized in a purchase exception granted by the designated central nonprofit agency.
Even if an exception is authorized, procurements must still be competed unless there is a an exception under FAR 13.106-1 and 6.302. Also, all acquisitions between micro-purchase threshold and SAT, are "automatically reserved exclusively for small business concerns and shall be set aside unless the contracting officer determines there is not a reasonable expectation of obtaining offers from 2 or more responsible small business concerns..." See FAR 19.502-2(a).