New lease agreements and increasing rent

[Bruce Shiba]

Context: House hacking with an owner occupied single family dwelling. One of my tenants lease will be up in June 15. Currently, month to month rent is the default option after the lease expires. 

I'm wondering if a) I can increase rent at all (or did I need to give notice 2 months in advance) and b) if the tenant signs another lease, can that be for higher rent (annual, month to month, etc.)

Essentially, I want a higher monthly rent payment for the increased exposure of not having a tenant for the entire year. 

Can this be done?... or does the existing lease that defaults to month to month supersede a new lease that's month to month?

Thank you!