Multiple Visas of different types

Hi, I'm a UK citizen and I'm going to be enrolling as a short term language student in Shanghai next semester. I'm getting the X2 visa for short term students.

Before I go, I'm going to be staying in Hong Kong and Shenzhen for a month as a tourist and want to travel between Hong Kong and Shenzhen regularly.

Would I be able to apply for the X2 and the multi-entry tourist visa at the same time? Using the tourist Visa when crossing from Hong Kong to Shenzhen at the rail border and then later use the X2 when I fly from Hong Kong to Shanghai?

Thanks :)