491/600 base (701 temp max) as a well-read dragon turtle - maybe.
As a 20th level bard, with True Polymorph, Hero's Feast, and Aid among your Magical Secrets, assemble an appropriate hoard of resources, cast a few spells into Glyphs of Warding (using scrolls where appropriate), then True Polymorph yourself into a dragon turtle (CR 17). That gives you 341 HP on the average numbers, or 450 on a max roll. Following that, spend the time to properly read and make use of 5 Manuals of Bodily Health, increasing your constitution (as a Dragon Turtle) to 30, and thus giving you an extra 5 HP per hit die - taking you to 451/560.
We can do a bit better than that if we don't limit ourselves to the Monster Manual, but it seemed that the question was about core books.
Boon of Fortitude, also post-dragon-turtle, gives us another 40 HP, taking us to 491/600. This is complicated by the fact that Epic Boons are only available to 20th level characters. Is a 20th level wizard who's been polymorphed into a Dragon Turtle still a 20th level character?
Aid cast at the 9th level from a Glyph of Warding gives you 45 hp. Heroes Feast from another Glyph of Warding gives you another 11.
Absolute max before temp HP: 656
If temp HP are included, it's just a matter of adding in a lvl 9 Armor of Agathys (again, Magical Secrets, Glyph of Warding, and scroll crafting are your friends) to crank the total up to 701.
There's a fair amount of cheese in getting to that 701, though.