Yes! We'll save 0.05%! That's 500$ for every million in sales. You must have huge sales to justify a switch.
When you call, they will ask you two important things:
1. What is your current volume (if you're looking at switching from someone else)
2. What is your chargeback rate? (How often do angry customers call the credit card company to issue a chargeback against you?)
If you are growing and have increasing transaction volume, and you aren't defrauding your customers, then you can absolutely get a lower rate than you're paying now.
This is true for so many things in business - the list price means nothing!