The month after next (the month following next month). Commonly used; synonymous with 'sairai-getsu' (再来月).
請求書の支払いは翌々月の末になります。
The invoice payment will be due at the end of the month after next.
旅行は来月か翌々月に行きたいと考えている。
I'm thinking of traveling next month or the month after next.
契約の更新日は翌々月に設定された。
The contract renewal date was set for the month after next.