Generally, when I'm putting together a pitch for more resources (platform or hiring), I include the following information:
Job description already drafted
How the KPIs we have set have impacted the business. For example, if you're looking for someone to run a reference program, I would say something like, our reference customers have influenced $X in pipeline and bookings, accelerated deal cycles by X days, and increased average deal size by X%.
Do some math to put together what the impact will be with an additional resource. For example, by bringing on additional headcount, we expect to support X% increase in matching reference calls, which should yield X% increase in the metrics above.
If you can get really specific about your pain point and how a new hire will drive business or tie directly to a strategic OKR, it will be much easier for leadership to see how increasing headcount brings them value. It will also set your new hire up for success because it makes the job description clearer and tied to your department's objectives.