One limitation of a Psion is that they get only so many powers known and you basically can't exceed that amount. But there is another rule, Independent Research - one week and 200 xp per power level - and you create completely new power, or duplicate the one that already exists. The question is, can you use it to learn more powers than you usually are able to?
Ask your DM
The independent research guidelines are intended to be worked out between a DM and a player to allow the player to do interesting or unique things with their character. This can, in some cases, be used to power up (or power down) a character if necessary.
But the Psion is a pretty powerful class. The limitation on the number of powers known is fairly tight, but it’s not nearly as tight as, say, Psychic Warrior or Wilder (who have real problems in this area). Psions can do very well on their allotted number. On the other hand, especially if you want some flavorful powers, maybe the DM agrees they shouldn’t “count” towards your limit, seeing as that limit is pretty tight.
Ultimately, though, the rules themselves do not automatically allow the Psion to exceed their limit, or to even use those rules. They only give suggestions to DMs for what the costs of that sort of thing should be when they want to allow it.
This is not entirely clear from the rules text.
An argument for it being possible to learn more powers than the Psion class table indicates by performing original research is that "Independent Research" is a subheading of its own under "Adding Powers" in the Psionic Powers Overview. Thus, using Independent Research, you could bypass the limit imposed by the "Powers Gained at a New Level" subheading in Psionic Powers Overview and the "Powers Known" clause in the Psion class description.
An argument against it being possible is that the number of Powers Known displayed on the Psion class table is just that, a number of powers known, as opposed to a number of powers learned, even if the Psion class description itself only references the method of learning powers described under the Powers Gained at a New Level subheading.
Personally, I would recommend against making independent research be in addition to what the class table suggests as a number of powers known, for the following reasons:
- Getting GMs to accept custom powers is hard enough without it being a direct increase of the character's power.
- There are numerous non-ambiguous ways a psion can use to expand his repertoire, through the Expanded Knowledge feat (a feat that is fundamental to the whole psionic system) and through Psionic Items. Of particular interest is the Power Stone, which has an additional benefit that Wizards can not easily replicate: Powers can be manifested directly from another's powers known.