Los Angeles LA RSO Property New Lease Allowed?

[David Shaw]

I own a 4-unit Rental Property in Los Angeles city that is covered under LA RSO (Rent Stabilization Ordinance). I have one tenant that has been there for 10 years so their rent is very low. They love living there but they want the unit updated, about a $50k cost. In exchange the tenant is telling me that they are willing to sign a brand new lease at market rent. 

The issue is that I don't know if I am allowed to make a new lease at a much higher rent price with the tenant since he is under RSO, EVEN if the tenant is the one wanting it. I have called LAHD (Los Angeles Housing Department), and they have no idea, apparently no one has seen this scenario, or they are just incompetent. 

Has anyone experienced this? Would I be able to create a new lease agreement with the existing tenant? Or is there a workaround, for example if they move out then move back in? 

Any advice would be appreciated, sad that the department responsible for such issues can't answer me.