Can you ever use an ASI to increase an Ability Score above 20?


My question stems from this one: Does the Star card from the Deck of Many Things increase your ability score above 20?


How exactly does increasing an ability score above 20, by any means, work at all?

Relevant quotes:

Ability Score Increases: Some of these features allow you to increase your ability scores, either increasing two scores by 1 each or increasing one score by 2. You can’t increase an ability score above 20. -PHB pg. 15

Manual of Gainful Exercise: …your Strength score increases by 2, as does your maximum for that score.

Say you have a Strength score of 18, and use a Manual of Gainful Exercise to increase it to 20, can you still not use an ASI to increase it to 22, despite the “maximum” now being 22? In fact, is 20 even the maximum for your ability score when using items; the quote seems to only apply to Class Features.