There is an exception if the club finishes in the "extra" place as the two extra places cannot be passed onto another league.
Yep - essentially the priority that places are assigned is:
1. CL Places awarded via UEFA multi-season coefficient (for England, top 4) - transferrable (but not really because they're awarded first)
2. Champions League places awarded to previous Champions League and Europa League winners - non-transferrable
3. CL Places awarded via UEFA single-season coefficient (which makes up the 5th spot) - transferrable
4. Europa League places awarded for multi-season coefficient (for England, 5th place in league + FA Cup winner) - transferrable
5. Europa League places awarded for previous Conference League winners - non-transferrable
6. Conference League places awarded for multi-season coefficient (for england, League Cup winner) - transferrable
Essentially places awarded via coefficients can be given to other clubs, places awarded via winning European competitions cannot.
What this means in short is that ...
- The Top 4 always qualify for the Champions League.
- The Champions League & Europa League winners *always* qualify for the Champions League, but their places can't be transferred so if they finish in the top 4, they're lost. As of such, from a maximising places perspective the best outcome is they finish 5th & 6th. It doesn't matter in which order.
- The 'extra' place then gets awarded. As 5th & 6th have already qualified, it drops down to 7th place.
- The Europa League places then get awarded, but are transferrable. So ideally the FA Cup winner finishes in the top 7, which gives 2 places to the league. 8th & 9th qualify for the Europa League
- Then, if the Conference League winner finishes exactly 10th (so doesn't qualify via the league or the FA Cup), they also go in to the Europa League
- Finally, the last Conference League place is transferrable, so as long as the League Cup winners finish in the top half of the table, the Conference League place goes to the team that finishes 11th.
1st-7th are in the Champions League, 8th, 9th, & 10th in the Europa League, and 11th in the Conference League.