Raising under market rents after purchasing multifamily

[Russell Lavoie]

I'm about to put in an offer on a house in Fall River Massachusetts and there are two long term existing tenants at will that pay 300-400$  less than market rent. I was told that I can only legally raise the rent 100$ at a time. The tenants are two clean single women. I'm not sure if they could afford market rent. My questions are, what's the best way to go about raising the rents closer to market value without losing the tenants? Should I screen the tenants after purchase to see how much they can afford? 

[Russell Lavoie]

wow thank you all so much this community is amazing. I really appreciate the responses so quickly!