
JDawg75 |

Primary rule is these must be permanent HPs. So no HPs from spells, SLAs, temp HPs , etc. Not even from a barbarian rage, as those are temporary, though if you want to include them parenthetically that's fine. You can assume max HPs per level, extra HP as FCB. Ideally this build will actually be viable for play, (e.g. a quality tank), but this is not required.
The basic benchmark is a 20th level Barb. Starting with a 20 Con going up to 25, a belt of constitution +6, Toughness, Finding Haleen trait, all FCB into HPs gives him 500 if I've calculated right.
J

Melkiador |

Is this just a thought experiment? There are a few options that are “temporary”, but also all day by level 20. A Goliath Druid could keep up Giant Form II all day for a +6 size constitution bonus to stack with your other bonuses. A kineticist could also have an all day +6 size bonus to constitution, but at the cost of taking a lot of nonlethal damage from burn, so it doesn’t mean as much.

avr |

Synthesist summoner might just win, depending how temporary their eidolon-suit is ruled as being.
Edit: 36 Con for your meat (20 base, belt, 5*+1/4 HD, wishes, greater aspect used for 3 ability increases on Con) w/toughness, finding Haleen and FCB and a d8 HD, max HP = 21*20 = 480 HP. The eidolon has 13 Con base, 3 increases at 4 HD, a +2 Con ioun stone, toughness, 1 ability increase and huge from evolutions: 20*15 = 300 HP. The total comes to 780.

BENSLAYER |

Although this is end of the line stuff, at Level 20 you can grab the Alternative Capstone Perfect Body, Flawless Mind (Ex) for a +8 Untyped to Constitution (if you so desire). If you allow Mythic, a Mythic Hero Tier 10 can gain a Permanent +10 Untyped Bonus to Constitution.
Shakier options :
* Have [Grand Hex] Force Reincarnation (Su) used by a Witch Party member/Ally repeatedly until you get a desirable new body. This is subject to G.M. co-operation. If given the go ahead, Reincarnate is a more expensive option, whilst the Salve of the Second Chance is a slower option.
* A Psychic 20 that chooses the Psi-Tech Discovery Artifical Ascension can hijack the body of a Robot, so your H.P. would depend on what you can take over. A Surgeon Robot is a Medium Construct with 179 H.P., (excluding an additional 75 H.P. Force Field).

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The 3.5 Living Arcanis campaign had a feat called Draconic Toughness. It was a fighter bonus feat. The first time you took it you got 3 HP. Second time you got 6. Then 9. So 18 HP for just three times. Oh, and 3 points from 3.5 Toughness too, so a total of 21.
Fighter build I heard was you just don't wear armor and put all your money into save boosting times and weapons.

Darigaaz the Igniter |

Alchemically Enhanced human gets you a +3 Con to start instead of a +2. Wish x5 gets you +5 Inherent Bonus to Con.
Exotic heritage to get the infernal(pit-touched) wild bloodline will give a +6 inherent to con.
21 starting +5 leveling +6 enhancement +6 inherent +8 alt capstone = 46 Con
Barb 20 = 20x12 + 40 FCB & Finding Haleen + 20 Toughness + 20x18 con = 660hp (720 when raging)
4 feats used: toughness, exotic heritage, eldritch heritage, improved eldritch heritage

DeathlessOne |

Hmm, I built something like this for a thread Before, something about "flubber award", that wanted to know how much damage it would take to outright kill a character. I believe I came up with effectively 1055 hp (assuming max hp per level, 100 of that is rage based), all without invoking Mythic levels, or multiclassing. This ... "finding Haleen" trait would boost that higher.
Was just a basic half-Orc Fighter (Viking)

avr |

DeathlessOne's Flubberoid. A lot of it's rage-related stuff (180 + DR?) but there's a protector familiar in there too, and advanced armor training options.

DeathlessOne |

Yeah, that's the one! Thanks for linking it. I lost the majority of my notes on it a while ago. It was a fun build. The main schtick I was going for was how far below zero I could pump that HP loss before s/he keeled over. That, and still being able to contribute in an above average way (average being expected CR-equivalent levels).