"with purpose to" is a correct and usable phrase in written English.
It is used to indicate the goal or reason for an action. For example: "I've been studying hard with purpose to get a good grade on the exam."
He fights with purpose (to consolidate Hindustan) but not without mercy.
It hired a designer, Martin Cooper, from Burberry to facilitate the transformation from garments with purpose to just garments.
"I offer my story now without rage, but with purpose – to share a tale that in its detail will reclaim my identity.
But where Mary J. Blige has made scorned pain her art, Beyoncé delivers heartbreak with purpose: to remind us just how overwhelming love can be.
In 2006, when he was twenty-one, he was arrested for "terroristic threats," a crime that in Minnesota encompasses behavior committed "with purpose to terrorize another or to cause evacuation of a building . . . or otherwise to cause serious public inconvenience".
Those in which the Jayawardenes batted could scarcely have been more benign, but they played with purpose to put Sri Lanka in a position where it could declare its innings closed with a day and a half left.
The "themes" for the Republican effort, for example, range from "Opportunity with a Purpose" through "Prosperity with a Purpose" to "President with"—wait for it—"a Purpose".
ADAM: Well, we farm with the purpose to make wine.
We were making clothing with a purpose to protect and follow the body.
This time they came with another purpose: to schmooze, impress and, perhaps ultimately, lure.
This time they came with another purpose: to chat, impress and, perhaps ultimately, lure.
