Any company that claims they can’t amend a contract is full of shit. That’s literally how business operates - they negotiate and change contracts all day long.
There are caveats, however. Making exceptions for employees can raise alarms in HR compliance. If an employee in a protected class has asked for the same, but perhaps cannot be granted the same terms, it could create liability.
Larger companies really, really don't like having terms vary across their non-executive level employees. And, arguably, for good reason.
Larger companies really, really don't like having terms vary across their non-executive level employees. And, arguably, for good reason.