Yes - in theory 9 is the maximum, but 8th can never make Europe.
From an article just published by The Athletic. If correct we are all West Ham and Leicester fans
And what happens if both teams win their competitions?
This is complicated. Let us start with what we know for certain — City, Liverpool, Chelsea, Tottenham and West Ham would be in the Champions League, while Arsenal and Leicester would be in the Europa League.
If Palace do not win the FA Cup, it means that the cup winners’ Europa League place would go to the next highest-placed side (Manchester United in seventh), seeing as sixth-placed West Ham would have qualified for the Champions League.
With Liverpool having won the Carabao Cup, earning them a place in the Conference League, their place in that competition would go to the team in eighth — Wolves.
This would see nine Premier League teams in European competition next season.
If Palace win the FA Cup they will join Arsenal and Leicester in the Europa League. Liverpool’s place in the Conference League from winning the Carabao Cup would go to United in seventh.
No space would open up for Wolves in eighth but again, nine English teams would feature in Europe.
We explain how the Premier League's European qualification places are shaping up for next season...
theathletic.com