So the best way to go about this would be to have a more successful Alexander Severus?
More or less. Barbarian invasion will still occur, but the empire might have an easier time containing the incursions.
Or, what if the Severans never take power? Caracalla increased the army's pay by like 50% or something, (which even though he probably did need to keep its loyalty is still a little overkill)?
Can't be helped. I recall one historian arguing that the service in the Roman army is getting less and less popular by the time the Severan dynasty came to power. If that is the case, you either accept a much smaller army or you increase the pay of the soldiers.
Another dynasty/Emperor would probably have done the same.