Adding an unauthorized tenant to lease & rent increase

[Lois S.]

We lease out a SF home in which current single tenant has resided for 4 years with minimal issues.  This is a no-pets property, clearly spelled out in the lease.

The neighbor contacted me to complain about a dog that's been in the unit for about 3 months & says it belongs to the tenant's family that has apparently moved in. 

We called tenant & she agreed to remove the dog & I mailed her a notice of lease violation.

At the same time she confirmed her child & 2 grandkids had moved in while relocating to the area to look for a place to buy. However, she also said the child is having a hard time securing a down payment. (Not surprising in our overpriced market.)

We've decided to work with the tenant & have her child submit an application & we'll run the usual credit/background reports.

I'm not thrilled to have 3 additional tenants because of added wear & tear.  Tenant does pay her own utilities/garbage. 

I've also been remiss in not raising rent for 3 years because I'd prefer to keep the tenant rather than have turnover.  (Yes, I know - my bad)

My partner wants to raise the rent if/when new tenants are added to lease. 

Is this legal or is it discrimination based on family size?I could just wait & raise it later, I suppose.

Would it be legal to raise the SD based on number of people in the unit?

*Thanks in advance for any thoughts on this subject.