The following info is derived from these stories: Jade 3, Jade 5, Jade 6, Ayla 4 p3, Ayla 4 p4, Reach 1, Sara 2 p3.
A common concept among certain super powers is the Body Image Template (BIT). The BIT is a theoretical concept where a mutant intrinsically develops a certain template model (the BIT) that is used to mold and control the mutant's physical body. If the body deviates from the BIT (e.g. injury), it will always attempt to revert back to the BIT (e.g. regeneration).
An exemplar has a fixed, strong BIT, which tends to be based on his/her subconscious ideals of a perfect body. A shifter, on the other hand, has a more malleable but weaker BIT; their BIT can be changed, sometimes at will. There is even a case of a shifter (Jello) who could be described as an anti-exemplar; her body lacks a BIT and even after BIT implants (see later), quickly reverts to a BIT-less state.
A BIT influences non-physical characteristics as well, including memory and Ki. In fact, it is theorized that certain engrams (memory fragments) of the mutant are largely responsible for — or at the very least, influence — the BIT; if a mutant's memory is altered (even through hypnosis), the BIT may change. The BIT is also related to psychokinesis (PK) — an exemplar's PK directly affects his/her own body. However, a BIT does not apparently influence other psychic powers, e.g. implanting a psychic mutant's BIT onto another mutant doesn't give that other mutant psychic abilities. Also, biodevisors claim that BITs are not biological; however, Knick-Knack's BIT-splicer throws some doubt on that assertion. (However, note that the BIT-splicer doesn't work, at least as of early January 2007).
There is much ongoing research on measuring, analyzing, copying, altering, and implanting BITs. Knick-Knack's BIT-splicer "splices" a BIT of a donor into another person. However, it's crude in the sense that it also tries to copy the donor's body's physical/biological/genetic features unrelated to the BIT, which must be crudely filtered out. BITs also seem to have an energy level associated with them. Jade's BIT energy level is exceptionally high (possibly enhanced magically), to the point that not even the whole campus can produce enough power to replace it (Jade also has a much lower BIT "waveform" that's associated with her repressed-shifter spirit).
A BIT can apparently be described mathematically (think string theory mathematics), but the mathematics require a higher amount of dimensions than reality provides. Thus, it can be said to be structured extra-dimensionally. Due to this, practically all magical attempts to change a persons BIT fail in some way or the other. Sara explains that a BIT may extend across infinite dimensions non-trivially, and thus would require infinite magical power to alter in a fully controlled manner.
An extra-dimensional density changer, such as Phase, can also interact with the BIT's extra-dimensional structure; specifically, when she's at so-called "disruption light" density, when she passes through a mutant with a BIT, she can distort that BIT permanently (see Tisiphone).
A mutant with a BIT that has inhuman qualities is sometimes classified as having GSD, but it is not technically GSD; GSD traits are genetic, while the BIT is not (at least not directly).
Here's the thing about BITs
Here's the thing about BITs. You don't understand them. Superintelligent paranormals in the WU don't understand them. We don't even have a system of math that can handle explaining how they function across dimensions. What we do know, from the best theories 'currently' put forward... is that the BIT is one part of a higher order of describing a being that is more than just physical dimensions biology. The BIT seems to describe how these beings are put together structurally in a way that is more controlling than purely genetics (ie genetics might give you blue eyes, but a combination of genetics, environment, health, and so forth will determine how well you see with those blue eyes... unless you have a BIT, in which case both the color and every other aspect of your eyes functioning will be defined by the BIT). We think.
We know that in some cases, introducing a change in the energy patterns within the individual in the dimensions above the physical and result in a change in how the BIT is expressed. But that's like saying, I hold a magnet next to my harddrive as it loads. Except to a ridiculously higher degree.
However, from observation, we also know that the energy construct that includes the BIT is not 100% complete in itself. If it were, there would more commonly be nothing left of the original human transformed by the process of linking with it (during manifestation). So, we 'assume' that during this energy surge of manifestation that links a human being with one of these constructs, that at least 'some' information about the original human is retained. And, in fact, similar lesser surges occur when mutant Shifters transform and to a lesser degree (in the opposite direction) when regenerators recover from major injuries... leading researchers to believe that these abilities require direct communication between biological processes and the energy construct containing the BIT.
Some 'limited' results in mapping these complex energy signatures can result in an artificial Shift or Regenerative cycle. But typically with a considerable range of failure.
Saying that Thulia's technique manipulates the BIT at the one time it is susceptible is a bit off... technically, she's manipulating the energy flare containing the information that makes the Link. As a result, when the energy construct binds to the manifesting mutant, it 'appears' to be connecting to someone who meets a different set of 'specs' than that individual may have displayed naturally. Thus the failure rate: that body's biology is prepared for a manifestation cycle that will leave it with one set of abilities... but has now been linked to a construct that does something else. And it has incorrect information for the default BIT mapping as well.
So, yes... its technically changing what the BIT will end up saying about that mutant... but its changing the course of the manifestation as opposed to the BIT. The result ends up as data in the BIT, but the technique will never work at any time other than during the manifestation process when that energy surge can be altered.
As to 'other' BIT altering processes... you'll note that the only way this generally works is as a device with low survivability rates. That's because you're talking about an energy construct that is multi-dimensional which is like a higher complexity version of the crystal computer/storage device Kryptonians use to store Ship data, AI's, etc.. and at our level of knowledge, trying to change one viable data set into another different viable data set is challenging at best... and we're trying to do it by holding a magnet next to the diskdrive while we transfer the file. And THAT is the best guess action of the most advanced gadgeteers and superintelligent paranormals. We don't even have the math to describe how to create the construct that holds all that data, let alone the code and storage data that's inside it.
And finally... from a META perspective.
The simple fact is, if it sounds like a stacked deck against the manipulation of the BIT... that's because it is. The WU is what it is BECAUSE there are few paranormals and power sets are limited and mostly random/uncontrollable. Introducing any option that is capable of reliably producing a paranormal, especially with a reasonably safe process... would irreparably change the universe and the power dynamics of the major organizations and political players. So you will never see a process by which we can safely make people manifest... or control manifestation to produce specific powers. Will occasional characters come out of processes like this? Yes... A number of the Gen2 authors went that route, though we tried to push them into other options. But the fact is, the next five or ten times someone tries Thulia's technique? All dead. If anyone other than Luke gets zapped by Jamie's gun? Dead.