CA After the 60 day notice to end tenancy. Can you extend tenancy

[Susan O.]

CA After the 60 day notice to end tenancy. Can you extend tenancy

Like after the 60 days are up can you then give a 20 day extension period where the tenant has to leave.  Then if they don't leave after those 20 days extended can you get the tenant to 

If you do that will it invalidate the original 60 day notice?  Also will the tenant have same rights within the original lease or could they just go into evictions if they also don't leave after the 20 days for instance?