There is no way we can tell you by how much you will be able to exceed your school's limits without risking damage to the airframe or other property, or injury to yourself or others.
Maximum demonstrated crosswind component means just that: maximum demonstrated. However, limits are set for a reason.
Yes, a good pilot might well be able to exceed the maximum demonstrated crosswind component and still fly, and land, without damaging anything. (Notice that I very deliberately do not say "safely" here.) Maximum demonstrated crosswind is supposed to be managable by ordinary human pilots, not requiring test-pilot skill levels or superhuman reflexes. Even limit speeds and loads are set with a safety margin in part because everyone screws up once in a while, even when trying to operate the aircraft correctly and within limits. That such safety margins exist doesn't mean that planning to exceed specified limits is a good idea.
Being allowed to solo during training doesn't mean being allowed to fly on your own accord. You'll still need to coordinate with your instructor, and if where you're learning to fly is anything like what it's like for me, the instructor will be watching and be just a radio call away while you're solo, just in case something goes wrong. Even longer-distance flying ("cross-country") solo before you have your license will require coordinating with your instructor, and you will almost certainly be limited in which airports you are allowed to fly to, precisely because the instructor needs to be certain that you can handle the conditions there. See Part-FCL.020(a).
Limits are set the way they are for a reason. Respect them. Go ahead and discuss with your instructor the reasons why those limits are what they are if you want to, but go into, and out of, that discussion with the knowledge that if you exceed them, you might get away with it some of the time, but you won't get away with it every time, and if you don't get away with it, the results can very easily get really ugly. Best case, you'll find yourself doing something like a dozen go-arounds in a row because you can't stabilize the approach well enough and don't have a well-established alternate you can go to. At that point, and with the fuel gauge needle heading steadily toward the red, will you be able to hold back the get-there-itis? What will that do to your ability to attempt to land the aircraft safely?
Quite frankly, if this question is indicative of your attitude towards aviation safety, then please do yourself, and others, a favor and stop piloting. You are going to get into an incident, or an accident. It's not a theoretical "slightly increased risk"; it's a very real thing. The simple fact is that landing with even a moderate crosswind (even more so if it's gusty, as it often is) is precision maneuvering at highway speeds, in a flight regime where you have the least precision available and the least margin within which to recover from an error.