"accept suggestions" is correct and usable in written English.
You can use it when you are asking someone to consider taking input from others. For example, "We are open to new ideas, so please feel free to offer your suggestions and we will accept them."
The S.E.C. will accept suggestions for another 45 days before approving them.
RIM indicated in the filing that it has no plans to accept suggestions from several dissident shareholders for new board members.
The Author will heretofore accept suggestions from concerned friends regarding certain moderate physical activities to improve "spirits" and boost "self-confidence".
Although he described the situation in Egypt as "very bleak", Hague said he did not accept suggestions that nothing could be done.
In 1714 he refused to accept suggestions by Robert Harley and Viscount Bolingbroke that he renounce Roman Catholicism and become an Anglican in order to be designated Queen Anne's heir to the throne of England.
While in a hypnotic trance, you are neither unconscious nor asleep, but rather in a deeply relaxed state that renders the mind highly focused and ready to accept suggestions to help you accomplish your goals.
It's possible that the sinister messages are the result of disgruntled Google employees, for instance, or that mischievous users are abusing the "Suggest an edit" button, which accepts suggestions for better translations of a given text.
However, the organisation has set strict rules for accepting suggestions from the public.
Corps officials made it clear that they were accepting suggestions and insights from the experts, but not unquestioningly.
Government has not accepted suggestions and bids for development work on sustainable improvement to social care services".
They resist accepting suggestions, thinking it will make them appear weak, and they don't believe that others have anything useful to tell them.
