Google/bing software vocal harmonizers and you will find a number of them with prices ranging from free to hundreds of dollars.

Personally I use Melodyne Editor. I copy the vocal track, raise or lower the copied track then examine the track and correct any notes that do not sound great. The software does not follow chords so you have to know what chords you are working with and when raising an entire track say a third all notes will be raised a third thus putting some in conflict. For example it may put a F in a D chord, thus you must raise/lower the F to a F# or E.

Melodyne is the best that I have found a creating harmonies, but even with it if you get too far from the original note(s) you will get anomalies.

Good luck.

Whenever I get something stuck in the back of my throat, I dislodge it by drinking a beer.
It's called the Heineken Maneuver.

64 bit Win 10 Pro, the latest BiaB/RB, Roland Octa-Capture audio interface, a ton of software/hardware