One good approach would be to conduct a facilitated meeting to collect and record all the ideas (e.g. brainstorming). Then, organize the ideas into a more digestible form and have another meeting until a consensus is reached.
Who has the final say on quality will vary greatly by industry. For example, at NASA, we know from past incidents that management can override project managers and engineers. In Pharma in the US, the FDA usually has the final say. Generally the best approach is for the project manager to facilitate reaching a consensus on quality with the project team, then making a recommendation to the project sponsor. The project sponsor will suggest next steps.