Plenty of Immortals Projects are the creation of new species. Its possible one of them has violated the rules and is producing Hercules type characters.
Scion of the Immortals Rules
by Sean MeaneyYou are of the scion of an Immortal, but that power comes with a curse... or two.
Apply the Artefact creation rules from Masters DM guide. Your starting character begins with a penalty and a Handicap as though you were a minor artefact. At zero xp you have no powers, just two curses. So now you must advance as a PC under a curse until you can trade 10,000xp for 1pp. At 10pp you can take a single 10pp power as a permanant ability though you might save up your pp until you can buy something powerful like Wish(100pp).
These pp recharge slowly over many turns so you have multiple uses per day.
Example: Waheed the Crippled: 1st Level Lawful Fighter; 7hp; AC5; S12, I11, W7, D7, C16, Ch13; club(1d4), clothes, boots, chainmail. Waheed is Scion of the immortal Al-kalim.
Handicap: Waheed is permanently afflicted by an incurable lameness of the right Arm and inflicts 1/2 damage with any two handed weapon or weapon used in his right hand. And cannot use a weapon and shield at the same time.
Penalty: every time Waheed takes a life he takes 1d4 damage as punishment. This injury can heal normaly.