If you have enough miles (and are eligible for the no charge redeposit for MP tickets) the safest approach would be to buy the new itinerary and then immediately cancel the existing reservation.

Once a ticket is issued there are a certain number of "coupons" (terminology remanent from paper tickets) associated with it -- with the exception of through flights (say XXX-ORD-YYY on the same flight number) there is one coupon per flight segment -- any voluntary change that results in a change to the number of coupons generally requires a new ticket to be issued (this is an "airline ticketing" not a "United specific" thing) so if you want to add a new segment to an existing ticket -- increasing the number of coupons required -- a new ticket would be required.

Even though United handles this behind the scenes most of the time its one more thing that makes this not easy(tm) -- and UA also forces inventory verification on a ticket reissue so if you have a segment currently in inventory that's not available UA will not rebook it (a talented agent can work around this but I would not count on that especially over the phone)