Both the opposition Democratic Party For The People (DPFP) and Japan Innovation Party (also known as Nippon Ishin no Kai, or Ishin for short) have said they will work with the government of the day on a policy-by-policy basis via a so-called “confidence and supply agreement” – instead of forming a multi-party coalition to take down the ruling administration.

Nonetheless, Dr Sota Kato of The Tokyo Foundation for Policy Research think-tank told The Straits Times that the situation “could be a positive” for Mr Ishiba if he plays his cards well.

"A week after election loss, Ishiba has a tailwind to form next government and remain as Japan PM," The Straits Times
https://www.straitstimes.com/asia/east-asia/a-week-after-election-loss-ishiba-has-a-tailwind-to-form-next-government-and-remain-as-japan-pm

Profile of Research Director Sota Kato
https://www.tkfd.or.jp/en/experts/detail.php?id=29