Does anybody know why would もう一枚 be used adverbially in もう一枚マントを出して? I've read that, if a numeral is placed before the particle を, you use の as in もう一枚のマントを出して.
It's not being used adverbially. The の was simply omitted as often happens with particles in causal speech. The grammar doesn't change. It is understood as being there by the hearer.