Present competition as an alternative to push for better pricing. Make it clear that another vendor has quoted significantly lower for similar functionalities, which will compel the current supplier to reconsider their pricing to retain your business. This is especially effective if you can demonstrate financial constraints from your organization, pushing for the most competitive bid.
In your upcoming contract renewal discussions, emphasize that you do not expect an uplift in pricing. Use past agreements and industry benchmarks to strengthen your position. If you can demonstrate that your usage hasn't significantly changed or is potentially lower, leverage that to reduce or eliminate the uplift you might face with this new agreement.
Emphasize the need to remove the auto-renewal clause from the contract to give your company the flexibility to reassess its options each year. This requirement from finance/legal will help you maintain power in the negotiation and review potential alternatives more freely at the end of the contract term.
If you plan to scale up significantly, communicate this growth intention clearly. Highlight your organization's growth trajectory and insist on a discounted rate as you expand. Utilize this as leverage in your negotiations for better terms as it ensures a long-term partnership.
As a tactic, offer to promote the software through a case study or act as a reference in exchange for more favorable pricing. This showcases your commitment to the software and can help persuade the vendor to align with your pricing expectations.