Time4Tea: I'm not sure I know the answer, but: which game are you referring to? This forum is for the whole ES series.
Nitecrawler: Cromm, my bad!
Oblivion.
I know going from 1 birthsign Stone to another replaces the former one.
I am doing thse fisits as some sort of role-play self pilgrimage, also to learn all the magical effects later for Enchantment. So if for Heaven Stones I can only "keep" one power actionable, than I shall leave the one I want for last.
-n
This is from UESP wiki
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Doom Stones
The Tower Stone just after dawn
There are two different kinds of Doomstones; the Birthsign Stones, related to the constellations that mark the zodiac of Tamriel, and the Heaven Stones, related to other celestial bodies:
Birthsign Stones grant one of several Greater Powers specific to that stone. These powers can only be obtained one at a time. For example, if you acquire Arcane Well from the Atronach Stone and then use the Lady Stone, your Arcane Well power will be replaced by Lady's Warding; you cannot have both. However, you may switch between Birthsign Stone powers as often as you wish, and using a Birthsign Stone will not replace the birthsign and birthsign power chosen at the beginning of the game (e.g., if you chose The Shadow at the start of the game and then use the Atronach Birthsign Stone, your character page will still list The Shadow and you will retain the Moonshadow birth power in addition to Arcane Well).
Heaven Stones, like their Birthsign counterparts, grant one Greater Power each. Unlike Birthsign Stones, the powers do not replace each other when a new stone is used; one may obtain and keep all seven Heaven Stone powers by visiting each of the seven stones.
Due to their greater power, Heaven Stones also have a Renown requirement, which differs by stone; the sum (not difference, as some sources state) of your Fame and Infamy must exceed the required number, or the Stone will, when used, display a message stating that "The Hero's fate is known when the Hero's fame has grown." The renown requirement can be met by wearing the Gray Cowl of Nocturnal reward from the Thieves Guild, as it gives you 100 Infamy whenever worn.
Both types of Doomstone can only be used at night, between 6pm and 6am. Attempting to use them outside these hours will result in a message saying "No stars shine upon the doomstone."
The powers acquired from Doom Stones also add the relevant spell effects to the list of effects your character knows, and therefore can be used when creating custom spells or custom enchanted items. In particular, Doom Stones provide one of the few ways to acquire the Fortify Skill and Resist Frost effects; they can also make Chameleon available to characters with low Illusion skill.