Can I increase an ability score over 30 with an item such as a Manual of Bodily Health?
[After reading] this book... your Constitution score increases by 2, as does your maximum for that score.
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Rules As Written (RAW) and Rules as Intended agree.
The PHB defines a general rule which says that the ability score maximum is 30.
A score of 18 is the highest that a person usually reaches. Adventurers can have scores as high as 20, and monsters and divine beings can have scores as high as 30. (PHB p. 173)
It then goes on to list a table, about which it says:
The Ability Scores and Modifiers table notes the ability modifiers for the range of possible ability scores, from 1 to 30.
This means that the PHB explicitly defines 30 not just as a maximum (as 20 is also described), but as the highest possible Ability Score. Nothing can go above it, not even a Tome/Manual.
Jeremy Crawford agrees in this Tweet:
Q: [A Tome/Manual] wouldn't allow a creature to ignore the max cap of 30, however, would it?
and this one:
Q: Can a Tome of Clear thought be used multiple times to bring a Stat above 30?
A: Ability scores can go from 1 to 30. See "Ability Scores and Modifiers" (PH, 173).
Both of which inform a later Tweet which says the same thing.
So it is clear that Crawford is saying that 30 is intended to be a hard cap for ability scores, which agrees with the RAW above.
This is despite the fact that the "normal" cap at 20 is by-passable. It seems that the limit of 30 is intended to be a hard limit whereas the limit at 20 is not.
This is speculation on my part, but it is likely that the reason there is a hard ability score cap is because of the 5e design philosophy of bounded accuracy.
Ability scores, even when you raise the maximum, can never go above 30.
Ability scores go no higher than 30. For regular folk, they go no higher than 20.
Q: It wouldn't allow a creature to ignore the max cap of 30, however, would it?
Checking the table of ability score modifiers in chapter 1 of the PHB, we see that only numbers between 1 and 30 are listed - and notably: even though 28-29 is listed for a modifier of +9, only 30 is listed for +10.
This isn't solid evidence on its own, but it backs up the interpretation of Crawford's tweet above.
Depending on how much stake you place in Crawford's Tweets, ability scores should be able to be increased past 30.
RAW ability scores should absolutely have no limit when using a Manual/Tome.
As others have mentioned the relevant general rule is that ability modiefers have a range of 1-30:
The Ability Scores and Modifiers table notes the ability modifiers for the range of possible ability scores, from 1 to 30 (PH, 173).
However, there are some specific rules that clearly override this general rule. The first being the Intellect Devourer's Ability, Devourer Intellect:
The intellect devourer targets one creature it can see within 10 feet of it that has a brain. The target must succeed on a DC 12 Intelligence saving throw against this magic or take 11 (2d10) psychic damage. Also on a failure, roll3d6: If the total equals or exceeds the target's Intelligence score, that score is reduced to 0. The target is stunned until it regains at least one point of Intelligence (MM 191).
As well as the Shadow's Strength Drain attack:
Melee Weapon Attack: +4 to hit, reach 5 ft., one creature. Hit: 9 (2d6 + 2) necrotic damage, and the target's Strength score is reduced by 1d4. The target dies if this reduces its Strength to 0. Otherwise, the reduction lasts until the target finishes a short or long rest (MM 269).
And for reference the text for Manual of Bodily Health reads:
This book contains health and diet tips, and its words are charged with magic. If you spend 48 hours over a period of 6 days or fewer studying the book's contents and practicing its guidelines, your Constitution score increases by 2, as does your maximum for that score. The manual then loses its magic, but regains it in a century.
So in conclusion, just as the Intellect Devourer's and Shadow's abilities bypass the "hard limit" on the minimum ability score, so should the Manual be able to bypass the "hard limit" on the maximum ability score RAW.