What it means
そうにもない expresses that something appears very unlikely to happen or that carrying out an action seems nearly impossible. It attaches to the masu-stem of a verb and is often used when the speaker judges the situation from available evidence. The particle も adds emphasis, making the assessment stronger than a neutral statement with そうにない. The construction itself is plain, but it can appear in a polite sentence by using そうにもありません.
Usage note
そうにもない is used with verbs, not directly with nouns or adjectives. Do not confuse it with そうもない, which can have a different structure and meaning depending on context.
How to use it
来月までに計画が完成しそうにもありません。
The plan does not seem likely to be completed by next month.
来月までに計画が完成しそうにもない。
The plan does not seem likely to be completed by next month.
