'reasonable suggestion' is correct and usable in written English.
You can use it when proposing a suggestion that is considered sensible and logical. For example, "I think it would be a reasonable suggestion to ask our colleagues for help with the project."
This is a reasonable suggestion but unfortunately, there are important reasons for viewing it with caution.
On Riverside Drive she'll think of her first therapist, how for years she shook her head no to every reasonable suggestion he made, until one day he suggested she should teach, how it was like she'd been pouring nickels into the same slot machine for years and it finally paid out.
But whether your brother will think that's a reasonable suggestion, only he can say.
Although the actors are not on skates, when the derby matches are being depicted, the performers vigorously swipe the floor with their feet, giving a reasonable suggestion of careering around a track on eight wheels.
Brown's reasonable suggestion – that McKinnon would plead guilty to hacking offences but would serve any sentence in the UK – was then snubbed by a secretary of state who this week has been lecturing Middle Eastern countries on tolerance and humanity.
"In this era of instant communications, I think this is a reasonable suggestion and it will allow us to honor a subject's lifetime achievements while their memory is still relatively fresh in the public's eye".
These seem like reasonable suggestions.
All are reasonable suggestions, and most can be supported to some extent by textual evidence.
So he could make reasonable suggestions to his student, this teacher tried on Mr. Keplinger's head contraption and tried painting with it.
On the contrary, in all of our meetings he seemed to present very reasonable suggestions and no one really suspected that he would be a future candidate for political office.
But Mr. Chiu said: "All of our measures of water quality show that there are no problems, and if JVC has concerns, they need to produce numbers and to make reasonable suggestions.
