I think that, if you're talking about LHR tower frequencies, the use of 'expedite' will probably be with reference to vacating the active landing runway.
If this is the case, we're just trying to get you off because the next one is tight up your chuff and the term expedite is NOT used lightly. No, there are no rules as to how many times you may use it in one shift, but to use it too often will ultimately demean it and therefore render it useless.
Any further, PM me.
P7