Since every voice is different and bridges/tessitura are in different areas can any piece be transposed to fit any voice type? If you have tenor singer "X" who alternates between head and chest voice a lot in a song and want to transpose it for bass singer "Y", you could just lower the piece sung by "X" to suit singer "Y" but will his bridges and tessitura all be the same relative to each other once the piece is transposed? I read that a bass singer has a wider "chest" voice range than a tenor but that a tenor has a much stronger head voice than a bass. If all this is true then wouldn't transposing be impossible since once the piece was low enough for the bass singer "Y" the head voice notes might be too low.
It's very dependant on a singer's range, and where the break point comes - everyone is different.
Changing the key will work for most songs, as most songs do not have a huge range - an octave and a half covers an awful lot of songs. The tessitura - the part where more notes of high or low pitch are found will confound some singers, but in a song with, say, a high tessitura, it may well be possible to drop the whole song some more.
So, by and large, yes, most songs can be transposed to fit most voices. The bigger problem that occurs is that when more than one singer is singing the same song, either in unison and especially in harmony. Occasionally in a situation where, say, four singers do this, the key may not suit all four. At that point, a harmony may need to be changed, someone is tacit for a few lines, and fun is had finding what is a compromise of key!