The phrase "accept a number of" is correct and usable in written English.
It can be used when referring to the willingness to receive multiple items, requests, or proposals.
Example: "The committee decided to accept a number of applications for the scholarship program this year."
Alternatives: "receive several" or "take in multiple".
He was obliged to accept a number of distasteful defenses, and he abandoned public life.
Sobhrang is involved in the women's charter movement that is pushing presidential candidates to accept a number of demands during their campaigning.
Bach fanciers happily accept a number of concertos that he arranged from works of others, among them Vivaldi, Telemann and Johann Ernst.
Landfills that accept municipal solid waste (MSW) in the U.S. may also accept a number of sulfur-containing wastes including residues from coal or MSW combustion, and construction and demolition (C&D) waste.
The committee's recommendation, that women ages 40 to 69 undergo mammograms every one to two years, rests on its willingness to accept a number of studies that the group in Denmark discounted.
As hard as it may be to accept, a number of the social workers involved in Peter Connelly's case, who have since lost their jobs, may have been among the borough's finest.
Editors say they have accepted a number of papers that reviewers have harshly criticized as unworthy of publication and have rejected many that received high plaudits.
The government accepted a number of the committee's other recommendations: it is improving debt forecasting and has set new debt collection targets for the Student Loans Company.
He accepted a number of important jobs of great diversity – in the fields of energy, information technology, broadcasting and public health.
As a result, the Mark II accepts a number of compromises in image quality in order to bring the computing requirements down to a manageable 16 megabytes per second.
Having retired from teaching three years ago -- at San Jose State University and at Mills College in Oakland -- he accepted a number of commissions to fill the income gap.
