Comb through full software ecosystem and do many hours of research to understand each potential competitor.
Put all competitors on a spreadsheet, and become an expert in the software category to compare the products.
Add criteria to the spreadsheet through your research of what each product does, based on research.
Score each product against criteria. Add new criteria as you research to score, go back and re-score each other product. Realize some are marketing jargon, remove and re-score products.
Contact internal power users and product owners. Convince them to do a review with you and develop a process.
Take in their criteria of why the teams have one product over the other. Do this for all products in comparison set.
Compare your criteria and scoring to the teams reasoning for needing their software. Go back to the teams with clarifying questions.
Realize some of the features they think are unique to their platform may be accommodated in the other platform.
Demo the other platform to be sure, take screenshots. Reach out to the vendors of the software, have one meeting to tell them your process. Have another meeting to do a demo of the product functionality.
Have a demo with the stakeholders to convince them they would be fine with the other product.
Make the business case to go with the product you think is best. As you bring it around for approvals, add to it, update it.
Transform the business case into a presentation, use this presentation to gather final approvals.