Oscar Wilde — Bigamy is having one wife too many. Monogamy is the same.
I would like to ask if I can paraphrase the first part of the aphorism without a change of the meaning into: Bigamy is having one wife in addition to that. The phrase “having one wife too many” seems to me a little bit unusual. Is it Wilde’s licence or is it standard English?
“One x too many” is a common English phrase meaning 1 more than whatever the appropriate number is. It is grammatical and clear.
In your modified version, when you say “in addition to that”, we don’t know what “that” is referring to. The sentence stops making sense, which makes the reference back to that sentence in the second part of the aphorism also not make sense.