"To support the suggestion" means to agree with and provide reasons or evidence to back up a proposal or idea. It implies offering assistance or approval towards the recommendation or thought being put forward. Full definition
Current research supports the suggestion that as dogs grow in size and their body ages, their requirements for vitamins, minerals and nutrients change. (nextgendog.com)
This research supports the suggestion that female lawyers opt out in response to pressure that occurs at the workplace level. (slaw.ca)