Would new pharmacy accept a jump from 5mg to 10mg pen?

Just wanted to know people’s experiences - I’m on my 3rd pen (2.5mg, 5mg, 5mg) and 2nd pharmacy. Do people keep jumping at this point to get the first time offers? Would a new pharmacy accept an order for a 10mg if my last one is 5mg? (Was thinking of stepping up using the 5mg to 7.5mg for a couple of weeks).