Generally speaking, it is possible. As far as I know, for example, Guangdong technicians, Shaoda, Han Shi and Mao are mostly allowed to apply for cross-majors, that is, as you said, you are a non-normal class, so you can apply for their school's enrollment major. Also, if you don't know, look at their school's annual professional enrollment catalogue. If you don't indicate the need for relevant professional applications, you can apply. Under normal circumstances, you can cross majors!