The phrase 'suggest to improve' is correct and usable in written English.
You can use it whenever you want to refer to someone recommending a course of action that would improve something. For example, "We asked the consultant to suggest ways to improve our safety protocols."
When it opened in Cardiff, Mollie Petrie, her singing teacher since she was 12, was in the audience: "I told her there was nothing I could suggest to improve it," she said.
What change(s) would you suggest to improve [class discussions/lectures/lab sessions]?
We suggest to improve the AV criterion via more realistic assumptions.
Which steps do senior medical students suggest to improve the use of the six methods of the cognitive apprenticeship model and the learning climate during clinical training?
Are there any changes that you can suggest to improve the way your patients are invited to/informed about retinal screening and the service delivered, which would improve uptake?
Some of the options we suggest to improve the overall picture are through raising the public and professional awareness, through adopting more advanced experiences from other countries, and through discussing the issues in appropriate medical and legal forums.
The improvement of land use management was suggested to improve the water management and maintain the sustainability of vegetation restoration.
Based on some theoretical work, an enhanced version is suggested to improve the approximation.
Meanwhile, some measures are suggested to improve the behavior of connection in resisting progressive collapse.
A specific modification was suggested to improve the efficiency of particle separation.
In this paper, quite a few original approaches are suggested to improve the previous MIP model.
