The SEA-TPE example you described is called "nested ticket". I've done it several times on CP before and not a problem. Since you are not returning to the original destination using your second ticket, that wouldn't even raise a concern.
If you are going to use seperate tickets and especially if you use different carriers, you must allow sufficient time to insure the connection. Having a backup plan doesn't hurt either
Exactly what I did last week:
Ticket 1: YYZ-SFO
Ticket 2: SFO-HKG-SIN-HKG-LAX
Ticket 1: LAX-YYZ
I just made sure I had enough time (5+ hours) between the flights on ticket 2 and ticket 1.