Can the word "majors" used as a verb be followed by "on"?

Neither is standard. The first is wrong; the second is borderline-acceptable.

"Acme construction specializes in quality remodeling and renovation."

"Acme construction prides itself on quality remodeling and renovation."

"Acme construction is known for its quality remodeling and renovation."

"Acme construction: Quality remodeling and renovation" (slogan, not sentence)

etc.

The usual idiom is to say that one majors in something:

Acme construction majors in quality remodeling and renovation.

The full sentence should be, "The major focus of Acme construction is quality remodeling and renovation." This indicates the majority of their work is focused on the discipline.

I am observing people struggling with proper word usage, at an alarmingly increasing rate. Simply following complete and proper sentence structure eliminates the majority of issues. (Example or rant? You decide.)

1: a person who has attained majority 2 a : one that is superior in rank, importance, size, or performance b : a major musical interval, scale, key, or mode 3 : a commissioned officer in the army, air force, or marine corps ranking above a captain and below a lieutenant colonel 4 a : an academic subject chosen as a field of specialization b : a student specializing in such a field 5 plural : major league baseball —used with the 6 : any of several high-level tournaments in professional golf

Source: Merriam Webster Dictionary