Work Permit question - Part time/full time

I'm currently living in Vancouver under a study visa, finishing up a masters degree.  For the past 6 months, I've been working an internship through my university, under the "on-campus work permit" portion of my study visa.  My internship is set to end at the beginning of June, but my company has expressed interest in hiring me on and sponsoring me for a work permit.  However, I'm hoping to focus on my thesis this summer and finish up by the fall.

So my question is, is it possible to apply for a work permit now with their sponsorship/LMO, begin working part-time this summer, then switch to full-time once I've completed my degree while still under the same work permit?  The employer would not change, just the hours.  Would that require a new work permit?

Thanks for the assistance!