'even may' is not a correct phrase in written English.
Instead, you could use 'even might' or 'may even.' For example: "My professor thinks I'm the best student in the class - he may even give me an A."
One day they even may hear my raps.
There even may be a bit of truth to that.
They even may be a bit silly, but proceeds go to help underserved public schools.
Police even may aggravate an existing prejudice, though they seldom generate prejudice on their own.
To the uninitiated, Dead Kennedys, Black Flag, Minor Threat – Crass, even – may have looked rightwing but were anything but.
And now, with only seven and a half months left as president, he even may want peace more than the parties themselves.
The nation's top lawyers may have broken the law, and even may have sent innocent people to jail, to advance the interests of the Republican Party.
As Newmyer admits, Marshall "showed little interest in preserving his papers for posterity -- and even may have destroyed some of them".
The tone of voice, a nuanced expression of affection, a joke even, may have been enough to soften Peter's 18-year-old heart.
He kept the staffer on the payroll and even may have brought the son Maria didn't know about into the house.
Thus complex geometries which even may vary in time can be treated efficiently using discretizations on a Cartesian grid.
