You can change the tube, capacitors, and change the sound maybe 5%. Changing the transformer helps a bunch, but then you are into adding maybe another $40 or so. That helps the sound a bit, but the real limiting factor from what I've found are the capsule and the grille.
The Chinese capsules most often used are centre-terminated 32mm. These typically have a raspy top end, and there's not too much you can do about that without changing the capsule's hole drillings. It may be possible to do some machining on the existing capsule (and replace the diaphragm - you have to replace it if you are taking the capsule far enough apart to do that), but I have not looked carefully at this. To accomplish this you need a very stiff, very accurate, lathe with a collet chuck - a 3-jaw will not work. The lathe I do capsule work on is accurate to about 5 microns, and you need that kind of accuracy. Obviously if you're getting this far into the capsule, you'll need new diaphragms. The original diaphragms aren't bad, but they aren't glued in, which means you can't re-tension them once it's off. I know somebody that makes diaphragms :green: but at this point you need to ask if it's worth it, and what you are trying to accomplish. If you want to make it sound a bit better, it's a case of changing the tube, transformer, some capacitors, and the circuit configuration a bit. If you want to make it sound really good, the biggest bang for your buck is the capsule, and that's where the costs (and/or work) go up a bunch.
The grille is usually also very dense, which increases the resonant effect of the air chamber around the capsule - pleasant on a U47 but not so nice on the Chinese ones. It comes from applying the paint on the mic after attaching the grille. Replacing the grille material helps, but then what are you using from the original Chinese mic? The power supply, frame, and body. If the mic you are looking at is the 'Apex 460', you can use the original PC boards with some mods, too.