The phrase "open to doing" is correct and can be used in written English.
For example, you could say, "I'm open to doing whatever is necessary to complete the project on time."
"I'm very open to doing whatever's suggested".
He said he was open to doing so again.
"But you know, I'm always open to doing [these] things.
Whatever is better for the team, I'm going to be open to doing it".
Mr. Stallman said The Times was open to doing a follow-up article, but not yet.
So everyone's open to doing a movie but there's no deal at this point?
Yes, the Trump campaign seemed shockingly and unpatriotically open to doing so.
Redknapp remains open to doing business in the January transfer window if he can find the right player.
"I'm open to doing a hearing every month, if that's necessary," she said on the ABC program "This Week".
I think we'd be open to doing something, some kind of TV special, I dunno about a movie.
Though Uber has declined to share user data with the Egyptian government, Careem was more open to doing so.
