Can a bid protest remedy be to add the protester as an awardee?

I apologize for only asking and rarely giving answers since joining. One day, soon, i hope to know enough to help others rather than only ask.

That said, Company A was one of 9 bidders on an RFQ. 3 bidders (including Company A) made the competetive range and gave final proposals. Terms of RFQ said that agency would make "up to two awards." Agency made two awards. Company A came in 3rd.

Company A got debrief and is considering protest. If Company A protests and the agency sees the grounds and realizes that it made mistakes and wants to resolve the protest w/o a decision, using a settlement or ADR, is it possible that the agency could say "OK, Company A, we'll make a 3rd award and give it to you"? Or, would do so be an impermissible change of the terms of the solicitation?

Much thanks,

John