"outright support" is a perfectly valid and usable phrase in written English.
You can use it when you are referring to an unequivocal endorsement or show of approval. For example: "The city council showed their outright support for the proposed legislation."
Russia, China, Lebanon, India, Brazil and South Africa have voiced outright support.
He expressed outright support for reproductive rights when he was governor of Massachusetts.
It gave the Liberal-SDP Alliance and their goals encouragement, not outright support.
Despite its outright support for Channel 4, the report did not let the broadcaster get away without criticism.
The interim Ukip leader has been expressing admiration, if not outright support, for Donald Trump over the last few months.
The Shiite-dominated central government in Baghdad has walked a fine line with its policy toward Syria, offering outright support neither to the Assad government nor the opposition.
Chandler, now serving his second term as governor, was angered by the choice of Wetherby, and most members of his faction either gave Wetherby lukewarm support or outright supported Cooper instead.
However, naturally, it is not being outright supported.
The large number of unauthorized immigrants makes it even harder, because many of them fear that outright union support could lead to deportation.
Conservative reliance on older voters has developed in parallel, and in Monday's survey the Tories command an outright majority support – 51% – of voters aged 65+.
Their plan called next for intensive work in Massachusetts, considered the most liberal state in the country, where they could expect courtesy if not outright public support from Sen. Ted Kennedy.
