"strengthen support" is a correct and usable phrase in written English.
It is typically used when describing actions taken to make something stronger or more effective. Example: As a manager, it is important to constantly work to strengthen support within the team. This can be achieved through regular communication, team building activities, and providing resources to help team members excel in their roles.
The lack of clear standards can actually strengthen support for government safety-net programs.
Your campaign may strengthen support for Mr Berlusconi from ordinary people like the man who cuts my lawn.
Reunion volunteers forge lasting connections between classmates, and strengthen support for the school and the reunion class gift.
New Cassini results continue to strengthen support for this model, and laboratory experiments back up our assumptions.
Opinion polls suggest a Tory government will strengthen support for independence, which currently stands at about 25%to28%8% in Scotland.
Mr. Gyurcsany had called for the vote of confidence to reinforce his mandate and to strengthen support for his program of economic austerity.
If the issue of the kidnappings is not resolved to Japanese satisfaction, it is likely to strengthen support here for economic sanctions.
Political analysts read the governor's actions as an effort to strengthen support among core Democratic groups, who have been lukewarm about Mr. Davis's re-election campaign.
Three months after "Fixing Intel" was published, McChrystal and some members of his staff flew to Paris to strengthen support for the war among French officials.
Varoufakis, who has warned austerity measures for Greece will strengthen support for the far right, told the broadcaster: "This programme is going to fail whoever undertakes its implementation".
Mr Corbyn is opposed to bombing in Syria because he believes that it could make the situation worse if indiscriminate or accidental civilian deaths strengthen support for Isis.
