In addition to the base meaning of
つつ ‘while doing (A)’ when used by itself, the addition of も simply adds the nuance of ‘even’. This is often translated as ‘even while doing (A), (B)’, or ‘although doing (A), (B)’. (B) will almost always be something that is somehow contradictory to (A).
Like
つつ, つつも will appear after the ます-stem of a verb that is the original ongoing action.
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一人（ひとり）で洞窟（どうくつ）に入（はい）るのは危（あぶ）ないと知（し）りつつも、入（はい）ってしまった。
Despite knowing that going in a cave alone is dangerous, I went in.
初（はじ）めてのライブで緊張（きんちょう）しつつもものすごく楽（たの）しめました。
Despite being very nervous at my first concert, I was able to enjoy it.
Caution - Like
つつ,
つつも will usually include a non-physical action in (A), such as reading, listening, looking, thinking, etc. (B) may be either physical or non-physical. Also, in the same way as
つつ is similar to
ながら,
つつも is similar to
ながらも.
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彼（かれ）は足（あし）を骨折（こっせつ）していながらも、大会（たいかい）に出場（しゅつじょう）しようとしたところ、監督（かんとく）に止（と）められた。
Despite having a broken leg, he tried to enter the tournament, but was stopped by the coach.
彼（かれ）は足（あし）を骨折（こっせつ）していつつも、大会（たいかい）に出場（しゅつじょう）しようとしたところ、監督（かんとく）に止（と）められた。
Even while having a broken leg, he tried to enter the tournament, but was stopped by the coach.
なんかこの話（はなし）は怪（あや）しいなと思（おも）いながらも、彼（かれ）のことを信（しん）じてみた。
Despite thinking, ‘this sounds fishy,’ I believed him.
なんかこの話（はなし）は怪（あや）しいなと思（おも）いつつも、彼（かれ）のことを信（しん）じてみた。
Even though I thought that the story was fishy, I believed him.
Despite the similarities, it will be important to remember that
つつ only appears with verbs, while
ながら can be used after almost any type of word.