A word of caution - there are big companies that always shop around for support contracts regularly, they always need 3 bids, before they justify re-upping with their current support contract. This is one reason we don't do support...
Large companies also do a lot of due diligence on support models. So there's a difference between Mongo Inc and the two freelancers .
I would suggest you think of your offering as a product, with a very clear value proposition for the service. Good reading on productized services [1]. What exactly do I get for my support contract? Why is it going to make me awesome?
Your unfair advantage is being smaller and hungrier. Really think deeply about whether you're able to commit to offer a high-touch level of service, and demonstrate this at every interaction. Work really hard on building trust[2]
1 - https://krit.com/blog/how-to-productize-your-consulting-busi...
2 - https://trustedadvisor.com/books/the-trusted-advisor