Is there a combat modifier, or other advantage, when stacking two or more battalions of the same regiment?
(other than there being 2+ units in the hex)
I don't see an entry in the rules about this.
No, the regiments are there for historical purposes.
If you mix divisions however you get a "Mixed organization" penalty when assaulting together.
There is no direct advantage, but there might be an indirect C&C advantage if a regiment holds a narrow frontage and a regimental HQ or divisional HQ is closer to its subordinate units.
Keeping units at maximum command range is possible, but I wouldn't recommend it for lower quality units as it decreases the chance they'll recover from Disruption.