電話のベルが聞こえたとき、無視しようかとも思った。
When I heard the phone's bell I wondered if I should ignore it.

We have 無視する = "to ignore",
無視しようか = "will I ignore it?"
無視しようかと思った = "I thought 'will I ignore it'".

I can't figure out what も is doing. Is it adding a sense of 'even'? As in 'I even thought that I should ignore it'?