Is this scenario in fact true in that you can take one requirement and compete it among two different GSA contracts?
If you have a body of work that can fit under two different GWACs (examples: CIO-SP3 and ALLIANT) could the effort be competed under both vehicles?
Is there a prohibition against competing one requirement on two vehicles?
What concerns would need to be considered?
If this is acceptable what are the necessary steps to make it work. Would the CS/CO need to get approval from the GSA or GWAC Contracting Officer? Would the terms and conditions have to reference the requirement was being competed on two different vehicles?
The benefits of competing a requirement apply to interagency contracting instruments such as GWACs just as they do with other types of acquisitions. For example, FAR 8.405-1(d)(3)
requires contracting officers to "Provide the RFQ to as many schedule contractors as practicable..." when using Federal Supply Schedules (FSS). While your question pertains specifically to GWACs, both GWACs and FSS are interagency contracts (ref. FAR 17.501(a)
Moreover, HHSAR 308.405-6 states "...the responsible program office must provide a written justification (emphasis added) for an acquisition under the Federal Supply Service program that restricts the number of schedule contractors or when procuring an item peculiar to one manufacturer." Again, while this applies specifically to FSS orders, it emphasizes the benefit of competing orders under interagency contracts.
The only prohibitions against competing your requirement would be if your activity was directed to order from one contract vs. another (CIO-SP3 vs. ALLIANT) for the items. The requiring agency's internal ordering procedures take precedence. You can learn more about GWACs on GSA's GWACs page.
There is also a "Chat" capability on the site to obtain more authoritative guidance on the topic.