To simplify:
If you want to change your ticket, in anyway, and it's a non-refundable ticket, you have to pay the change fee of $150 ($250 for International). This would apply in all situations with the following exceptions:
- You can use Same-Day Confirmed to change (no change in O/D locations) for $50 (free for GM, PM and DM)
- You can re-deposit miles from award tickets (as a PM or DM) for free.
AMEX Companion tickets are "use it or lose it" You technically can't change anything.