[verb ます-stem] + ながらも [i-adj] + ながらも [na-adj] + ながらも [noun] + ながらも [noun] / [na-adj] + でありながらも
ながらも means "although", "despite": the first part is true, and the second holds anyway, which you might not expect. A verb goes into the ます-stem, an い-adjective stays in the dictionary form, and a noun or な-adjective takes ながらも directly, with no だ or な.
Plain ながら after a verb usually means "while": two actions at once. ながらも only means "although", so the も removes any doubt. After a noun or an adjective, ながら alone is already "although", and も adds weight.
ながらも belongs to writing, speeches and careful speech. In conversation the same contrast is のに or けど.
A noun or な-adjective can also take でありながらきごう(もきごう), which is more formal still.
The set phrase ざんねん残念ながら "unfortunately" does not take も: ×残念ながらも.