I am sure large companies have that lever: I know of a large multinational company (around 150,000 employees along all contintents) that moved from SuccessFactors to Workday. Those are huge contracts.

Reasons for switching contracts can be numerous, and, from my experience, the level of support and quality of the actual application is rarely one of such reasons.

Yes, custom B2B support contracts that deviate from the terms of support that everyone else gets is not unusual.

For example: a large organization might get a "Microsoft Custom Support Agreement" if they want to get security updates after the date that MS stops providing security updates.

As with any negotiation, if you have leverage (i.e. dollars), you can negotiate.