Increasing Bitrate on mp3s

I have some old songs on my computer that are mp3s. They are only 96 bitrate. I have tried to find higher bitrates to get better sound quality, but have been unsuccessful, so far. It seems the older the song the harder it is to get it at a higher bitrate. At least that has been my experience, thus far.
So, I've done a little research. I read that increasing the bitrate on an mp3 DOES NOT improve the sound quality of the mp3. I was rather surprised by this, but it does seem to be the case. In other words, using an audio converter and taking an mp3 at 96 bitrate and converting it to, say, 192 bitrate will not improve the quality to what you would get for a 192 bitrate mp3. I've tried it several times and do not notice any significant difference. All it does it take up more space on my hard drive, increasing the file's size.
This is a shame. You would think there HAS to be a way to improve the sound quality of a lower rated bitrate mp3, but right now, I don't know of a way. That is why I am posting this, to see if there IS a way. Maybe there is a way to improve the quality, which doesn't involve increasing the bitrate, which as I said, doesn't work anyway. Is my ONLY alternative trying to find the mp3 at a higher bitrate?? That's tough! I am hoping you can tell me a way...a software, preferably free, I can download that can help improve the quality of these low bitrate mp3s I have. Thanks for your help and any education you may pass my way on this issue.

 

There is no way. The mp3 format is a 'lossy' format. It removes some of the audio information in order to get a smaller file size. The lower the bitrate, the smaller the mp3 and the more audio information lost. There is no way to get back this information once it is gone. You will have to find a better quality source.