The short answer is no, that's why we make different types of microphones!
With that said, providing you pick a microphone that doesn't have an obvious tonal character, you can usually match its characteristics to a recording to a useful degree by how you position it. For example, cardioid mics all exhibit a bass boost when used close up due to something called "the proximity effect", so if your mic sounds too bright (lacking bass) with a particular recording, try getting it closer to the source as this will warm up the sound.
Cardioid mics also have their best high end response on axis so you can reduce the amount of high end by twisting the mic around slightly so that the signal is directed slightly into the side of the mic rather than directly into the front. Placing a thin, vertical physical obstruction right in front of the mic, such as a plastic pen, also tames the high end slightly and can even help reduce sibilance.
When you need to achieve a brighter effect, you can use a broad EQ boost at 10 to 12kHz to add what engineers call 'gloss' or 'sheen' to the sound, but be careful with EQ, if you add too much it will sound harsh or shrill.
The real answer is that different microphones have different tonal characteristics, so the best way to achieve the perfect sound is to try out the recording with a range of different microphones and then pick the one that suits best. If you are running a home studio to produce your own music, then you can pick whatever mic works best for you, but in a professional facility, it helps to have a range of different microphones available.