Besides saying No, it’s worth considering a “Free Ice In Winter” approach.
By that I mean, a short window of exclusivity for a top customer or partner is often OK in the real world — in the early days.
If you don’t have have a similar prospect in the pipeline, giving a 3–6 month exclusivity window might not be the end of the world. You might not even be able to deploy anyone else until them.
At the end of the day, Big Customers and Partners understand you have to run a business. It is also not unreasonable for them to want some of the benefits from their investment in you. Finding a short-ish period in the middle often ends up being fine in the real world, vs. being dogmatic on no exclusivity at all.