You can do it all you want and nobody is going to care as long as you don't have any checked luggage. I do it probably 1-3 a year for various reasons, mostly involving change of plans and it just being cheaper to buy a new ticket. Say, if I originally was booked IAD-DEN-SEA-DEN-IAD and somewhere along the trip I found out that after SEA I needed to go to DFW. I would just buy a DEN-DFW-DEN-IAD ticket and toss the last portion of the DEN-IAD on the first ticket. I've always gotten the miles for the parts I've flown - and sometimes even the miles for the parts I didn't fly.

I'm sure you'll find many people here who toss the last leg of thier flights occasionally.