According to the PMBOK Guide, a project manager should recommend to the sponsor to review the results of the team's supplier evaluation, when faced with the situation of the sponsor requesting to add another supplier who has lower costs but does not always fulfill the project requirements. This is part of the conduct procurements process, which involves obtaining seller responses, selecting a seller, and awarding a contract.
The project team should evaluate the potential suppliers based on the source selection criteria, which are the factors used to rate or score seller proposals. The source selection criteria may include cost, quality, technical capability, schedule, risk, references, etc. The project manager should communicate the results of the supplier evaluation to the sponsor and other relevant stakeholders, and explain the rationale behind the team's preferred suppliers. The project manager should also highlight the risks and trade-offs of choosing a lower-cost supplier who may not meet the project requirements. The project manager should seek the sponsor's approval and support for the team's decision, and address any concerns or objections that the sponsor may have. This approach ensures a transparent and objective process for selecting a supplier, and avoids potential conflicts or misunderstandings between the team and the sponsor. References: PMBOK Guide, 6th edition, pages 479-480,
485-486.