Be prepared to move elsewhere if they attempt to raise the price. Create an artifact like a spreadsheet to model whether moving is worthwhile (considering the time and effort required to migrate) if asking for a concession on a price increase is unsuccessful. Also, use price/cost intelligence vendors to understand what others are paying for the SaaS when possible for negotiation purposes. Treat your vendors like they are commodities whenever possible to defend against vendor lock in risk. Long term contracts (~3 years) with capped increases tied to inflation are also a potential option if your vendor offers it.
The counterparty with the most leverage and who cares the least is the one who usually wins. Be that counterparty when you can.