The most important consideration is whether the Government follows (or at least does not violate) the evaluation method stated in the RFP. The RFP mentioned "staggered awards" and that's essentially what you are doing. So the better question is: Does anything in FAR 15.306(c) or (d) prohibit the additional evaluation of offerors so that any not immediately awarded a contract can subsequently be included in the next competitive range? I see nothing explicitly prohibiting that.

There could be an issue if the second set of offerors was allowed to submit FPRs to fine tune their proposals (e.g., submit more competitive pricing) when the first set of awardees did not have this opportunity. However, this is probably not relevant since each awardee (from both stages of the competition) should have the opportunity to submit “fair opportunity” task order proposals iaw FAR 16.505(b) and fine tune their last proposed prices. Since this issue has a potential legal implication, I recommend that you also consult with your activity's legal counsel.