"not necessarily support" is a correct and usable phrase in written English.
You can use it when you want to express that something might not necessarily be the case or provide support for an argument. For example, "The high price of the product does not necessarily support the quality of the item."
Mr. Rudman said he would not necessarily support either proposal.
For one thing, Mr. Kostunica is a Serbian nationalist who does not necessarily support the NATO presence in Kosovo.
They note that her wavering support reflects the nature of the women's vote in general, which does not necessarily support women, particularly in New York.
Only five Senate Democrats campaigned for him in last year's general election, and he has said that he will not necessarily support the next Democratic nominee for President.
Whereas many vendors and industry commentators tend to see cloud as being well progressed within organisations, real-world feedback does not necessarily support such a view.
"For people who believe that it's inevitable that a horrific experience like this would leave lasting scars, the evidence does not necessarily support that".
And they are telling Mr. Erdogan that while they may vote for him, they do not necessarily support all his policies.
But while Cermaq has accepted the study's findings, Chile's own National Fishing Service, Sernapesca, said it did not necessarily support them.
[Q: do you support Muslim state schools?] I do not necessarily support Muslim schools, but in the Belgian system it is logical.
These allies' interests differ -- and they do not necessarily support Napster's business -- but each has asked the court not to limit too narrowly the exchange of copyrighted works and information over the Internet.
They have determined, he said, that the book can remain on sale as an alternative theory to Grand Canyon history -- but one that the Park Service does not necessarily support.
