The biennial arts festival is known for staging world premieres with stars like Sir Kenneth Branagh and Maxine Peake.
The new project, titled Festival In My House, will see artists, performers and audiences invited into ordinary homes.
Residents can come up with ideas for shows they would like to stage and one such event will take place every month.
"It could involve flying somebody in to do the headline act in their living room," festival director John McGrath said. "But the budget's not huge - it's Â£1,000 for people to spend each time.
"Like us, they need to work out how to make their money stretch as best they can. And we support them every step of the way with that."
A producer from the festival will help the chosen householders book the right artists and performers and work out how to stage the event.
"They will help people get their ideas together and test whether they're the right ideas and give technical support," said McGrath.
"So people can think, do they want to use the table lamp to light that show, or is it best to do it by candlelight?"
The events could be one-off nights for neighbours, or longer runs open to people from further afield.
Two pilot events are taking place in the next two months: a celebration of music and food from different countries in a house in Cheetham Hill, and a festival of South Asian mehndi hand tattoos in Levenshulme.
Details of the Festival In My House project were released as the festival announced the first shows from its main 2017 line-up, which include:
The Manchester International Festival takes place from 29 June to 16 July. The full line-up will be announced on 8 March.
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Manchester residents are being asked to open their doors to host "micro" offshoots of the Manchester International Festival in their homes.