Meaning of "とも思う"


I'm not sure about "とも" in this sentence.

> そんなことを聞いては失礼か **とも** 思ったが、どうしても聞かずにはいられなかった。

Can anyone explain the usage of とも




It can also be written as:

> 『そんなことを聞いては失礼か』とも思ったが、どうしても聞かずにはいられなかった。

The と is the case particle as a quotative marker, and the も is the binding
particle. I think it's like "I also thought that it might be rude to ask such
a thing, but...", the "also/も" implying that you were thinking about other
things, too.

