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The answer is yes, but there "ifs" involved.
There is nothing in federal law disallowing a contractor working more than one federal contract at a time. So this may be done under the law.
However, if either (a) the contract itself or (b) the intermediary company prohibits being contracted with another agency (any, or government specifically), then this would not be allowed per contract. If nothing in any contract states this, then theoretically one is allowed.
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