Presenting competition as an alternative has shown great effectiveness in negotiations. Highlight any comparable vendor quotes that are significantly lower, as this will create urgency for the current supplier to compete on price. Specifically mention the functionality you are evaluating and the quoted figures to press for better terms.

Request the removal of auto-renewal clauses due to finance/legal compliance. Emphasizing that you cannot proceed with any contract that includes an auto-renewal can help leverage better terms. This tactic can simplify future negotiations and offer more flexibility in controlling costs.

Anchor your negotiations by stating that you were not expecting any uplift based on your budget and historical contractual agreements. Pressure on the notion that long-standing partnerships typically reward increasing volume with lower rates rather than upping prices.

Request a detailed usage report to validate how much of the service you actually use. If you find underutilization, leverage this with your current supplier to negotiate better pricing or credits for unused services, ensuring that you are not overpaying for features you don't utilize.

Offer to act as a reference or participate in a case study in exchange for better pricing. This will not only increase your value to the vendor but can also help you secure monetary concessions or better service terms in return.