|Re-encoding will do nothing to improve the quality of the sound and may even casue a deteriation.|
The only way you can record at a higher bit rate and inprove the quality is to do it on the original. The orginal will be a wave file that does not use compression. But even the quailty there will be depenadent on the bit rate used originaly.
MP3 uses what is known as lossy compression. That means that some of the information is lost during the intial recording compression. This works becasue the human ear is very good a filling in the gaps when it comes to audio. You cannot recover something that no longer exists.
This will explain the complexities of audio recording.