Spoilers for Madoka and Mai Hime, which are very good shows and which you should watch instead of spoiling yourself on
So the core part of the system is that becoming a noumenal girl requires that there is some other person whom you become a noumenal girl for. Becoming a noumenal girl causes you to acquire a noumenal companion animal who fights for you. It does not exist in the phenomenal world, only the noumenal one. Its appearance and behavior is basically a manifestation of your mental/emotional state, and how much power it has to throw around is a function of how strong your bond is with the person for whom you are fighting (or more particularly, how strong your will to fight for them is). You can control it by giving it commands, and more powerful familiars can respond to telempathic or telepathic cues. In the same way that you are your soul, not your body, you are your familiar, not your body. The process of becoming a noumenal girl takes your will to fight for this other person and uses it to give your soul this particular manifestation. It's made of noumenon and can only interact with noumenal things. Most people can't perceive it.The noumenal plane exists in the same physical space as the phenomenal one, and contains noumenal representations of the things that exist in the phenomenal world. The noumenal world is shaped by peoples' thoughts and emotions, and can shape them in turn. For example, a person sitting in a room feels relaxed in the room, and associates the feeling of being relaxed with things like trees and plants. They leave a noumenal impression of trees and plants behind in the room, and someone else who comes by then might get a very light mental/emotional suggestion of the concept of trees and plants, which has less pleasant associations in their mind, and they begin to feel agitated without consciously knowing why. The noumenal world mostly resembles the phenomenal world, because people mostly think that the world is at appears to their senses, but emotions and daydreams and stray thoughts still get out and affect things.
Whether a person affects the local noumenal landscape or is affected by it is essentially a function of their native noumenal energy potential and their sense-of-self. People have a little psychic bubble around them of their own thoughts and feelings, which corresponds to their soul. Some produce more noumenal energy and thus leave more in the wake of their bubble, while some produce less noumenal energy and thus leave less in the wake of their bubble. Additionally, the bubble is sortof like the AT field in NGE - it represents an ego boundary. The stronger your sense-of-self, the more solid and less permeable your bubble is. A person with high noumenal energy potential and a weak sense-of-self leaks noumenal energy everywhere; a person with a low noumenal energy potential and a weak sense-of-self is highly susceptible to outside influence. People with a strong sense-of-self leave less of a noumenal trace and are less affected by the noumenal world.
Your ability to sense the noumenal world is related to the permeability of your bubble. Those with very solid bubbles exist in a noumenally solipsistic state because they are so unaffected by the noumenal landscape around them that from their perspective, the local noumenal landscape is just their own mental landscape. Those with very permeable bubbles are so consistently affected by the local noumenal landscape that it essentially becomes just another input stream for them. Those in the middle can potentially learn to perceive the noumenal world, but on their own typically just assume that anything unfamiliar in their mental landscape is a part of them, not something externally originated. Those who are highly self-aware are more likely to recognize when something in their mental landscape did not originate from themselves, and thus are more likely to notice the noumenal world. With proper training, someone can make their bubble one-way permeable, or selectively permeable, but it is hard to do.
Noumenal girls give up the natural mental defense of the bubble in the creation of their familiar. Essentially, their bubble turns into the familiar, leaving them more vulnerable to noumenal attack, but with an active defense that they can use to guard their charge as well as themselves. Noumenal girls whose familiars die essentially become soulless husks. Noumenal girls whose bodies die are souls without a connection to the phenomenal world, and are likely to go feral and become dangerous. It is also possible, although rare and difficult, for the bond between a noumenal girl's soul and body to be severed, leading to BOTH a soulless husk of a body AND an aggrieved and potentially deranged familiar. A bodiless familiar will generally try to carry out the purpose for which it was created - ie, protection of the person they chose to fight for. However, it is also very likely to quickly lose its grip of what exactly that means.
Noumenal girls are typically more noumenally sensitive people, who can observe that the person they care about is being noumenally targeted, and choose to defend them from that. However, those who are not natively sensitive can still become noumenal girls - it's just that they're less likely to be aware that someone is in noumenal danger and needs defense. Once someone is a noumenal girl, they become fully aware of their noumenal surroundings, because they lack the ego-boundary that buffered them from the noumenal world before. Whether this simply grants them heightened noumenal perception or causes them to experience something akin to schizophrenia is basically a matter of how they interpret the new input. Those who were previously highly sensitive typically have an easier time adjusting, while those who were not can experience something like extreme sensory overload, and some never manage to learn to process the new data. It is most rough on those with a strong sense-of-self and low self-awareness - those who previously existed in noumenal solipsism - because they are most likely to interpret the new information as themselves hallucinating and 'going crazy' rather than as them simply perceiving new information about the outside world.
It is possible to manipulate noumenal energy without being a noumenal girl. This is done through careful control of your mental/emotional state and your ego-bubble simultaneously. By learning to have vividly imagined, intensely emotional thoughts at will, and then let precisely what you intend out of your bubble while letting nothing in, you can have subtle effects on the world around you. This technique can be used to cultivate or architect the noumenal landscape - this can be advantageous in noumenal combat, because you can alter the terrain to your advantage, give yourself noumenal armor, and so on, and anything which exists on the noumenal plane will have to overcome those things in order to get at you.
However, affecting the landscape also subtly affects the mental states of those who pass through. Those who are skilled in this sort of noumenal technique can use it to influence other people to feel or think certain ways without those people being aware that they are being influenced. This sort of influence can range between "I just feel comfortable and safe and pleasant in this place, I'm not sure why; I guess I just like it here" to "I really feel like there ought to be a big skyscraper here, but it's clearly a park, and something doesn't feel right about that; I guess I'm in favor of that bill that would allow people to build skyscrapers here" to "that person is smaller than me and doesn't look threatening, but man do they feel big and scary and intimidating right now; I think I'll back off and go bother someone else" and more.
Creating noumenal constructs is only possible through the intentional and extreme manipulation of other sentient beings, followed by killing their bodies. Essentially, a noumenal manipulator convinces another being to, through a similar process as a noumenal girl turning her bubble into a familiar, alter their bubble into the desired sort of construct, and then severs the tie between the two. Creating constructs in this way is dangerous, because unless the noumenal manipulator has done everything with extreme care, the resulting noumenal creature is likely to be violently unstable, and especially likely to be hostile towards the manipulator rather than loyal to them. Those who can achieve this feat are essentially masters of brainwashing, cult leaders, etc.
So, that's what I've come up with for the magic system, so far. I have a few ideas on the world and its history, and basically none on potential characters or plots.