Two Schools, Two Work Permits?

I have an ARC etc with one school and want to work for another school part time, in addition, who want to employ me legally. What happens with the two work permits, as in how do you apply exactly? He says I have to get two different work permits and ARCs, but that doesn’t sound right. What do I need to provide the second school with to apply for the legal work permit or whatever I’ll be applying for? Can my first school find out about the second?