This response is based on the information provided.  We suggest you discuss with your contracting team, program manager and/or legal department as appropriate. 

We do not have insight to any practices at NIH.  It seems as if you would like to compete a task within the scope of the task order you awarded and then award to the winner.  We suggest  you create your competition/solicitation as normal using the less detailed FAR subpart 16.5 Fair Opportunities procedures.  Put all offerors on notice you intend to select a winner and will modify the existing Task Order of the winner.

Please check with your legal to ensure there are no NIH policies precluding this approach.