You can do this via a filter. There's lots of advice on here and in the manuals about filters. I'll add some URLs below.
However, I wondered if what you really want is the urgency to change or the associated SLA / escalation actions? So for example, you still have a choice of urgency options that are the same for both Alpha and Beta customers but you pick Alpha customer and select Very Urgent it will apply a Priority 1 SLA but if you pick Beta customer then pick Very Urgent or if pick Urgent it will always still only apply a Priority 2 SLA. If this is what you are after then you need to look in the Administrators Manual under Response Agreements.
If you still want these, here are the articles I mentioned about filters: