Do we can compress mp3 files without loosing sound quality?
In short: Practically NO.
MP3 is compressed music. Some music formats do compress better than MP3 like AAC etc. but are only marginally better.
Also you should not do Post-Processing on mp3's
i.e.do not try to compress mp3's, change format, change bit-rate etc. this will lead to drastic loss of quality.
Though there are other formats, today the de-facto standard is 128kbps (bitrate) MP3 for music, higher bit-rates are preferred upto a maximum of 320kbps.
If you have only mp3 files, forget about more compression.
On the other hand if you have audio CD's [non-mp3, the proper audio CD] then you can 'rip' them to a better format/bit rate.
NOTE:DO NOT TRY TO CHANGE FORMAT/BITRATE OF MP3 FILES, ANY CHANGES WILL LEAD TO DETERIORATION OF QUALITY. Even increasing bit-rate to 320kbps using 128kbps is useless. you cannot bring back information [or 'music'] that was destroyed while creating the original MP3, except by maybe making A.R. Rahaman sing again!! :) !!
The above fact about loss of quality is because MP3 is a LOSSY compression algorithm, it destroys information in compressing music, UNLIKE .ZIP etc. where you can 'UNCOMPRESS' there is no such thing for mp3.
Please leave your comments IF YES or your suggestions on this.