Can a procurement method (strategy) on a firm fixed price DBB AE contract change at different phases of the contract?
Changing procurement methods at subsequent phases of the facility design and contruction is more likely to be a problem of funding than a matter of design approach. Each "phase" must reach the standard of "complete and useable" in its own right. Failure for a phase or stage to reach this operational capability raises the very specific question of incrementing your project so to remain under a statutory funding threshold - which violates most every one of the fiscal laws 31 USC 1301 / 1502 / 1341.
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On a more practical note, the two main techniques Design-Bid-Build uses the Brooks Act to contract for the professional design services; design build uses the construction contractor as the prime and the AE as a sub or partner (but the AE cannot lead see FAR 36.209).
Changing from DBB - wherere the design is final before soliciting a construction firm - to DB does not generally make sense late in a project. Although not prohibited, as a practical matter this becomes Build-(and then finish the)- design. The almost inevitable result is a poorly concieved building.
The benefit of starting a project as a DB is in recieving the construction/designer synergy throguht the life of the project. Starting late or with an almost fully designed project, leaves very little room for creativity.