First deal: Low existing rents, zoning breach

[Daniel Hynes]

Hey gang! 

First deal I've ever analysed. First potential RE purchase. First ever forum post... It's all terribly exciting and yet I'm sure I'm overly exposed to risk/exploitation as such a newbie. 

Problem 1: Low Current Rent + Rent Control 
As I look deep into this potential triplex, I see that current rents are way below market levels but I am in rent controlled Long Beach, CA. I can only legally increase by 5% + (% increase in cost of living), capped at 10% total. What I have thought of so far is to go way below asking and additionally bank on raising rents 5-7% every year until the cash flow becomes meaningful. What approaches do BPers have for this situation of underpriced rents?

Problem 2: Zoning Breach 
I dug into the city zoning codes and it looks like in this zone triplexes are not allowed! Zone is CNR in Long Beach, CA. I imagine this might be a source for leverage if approached correctly. I am not a unit short legally since the building is divided into 3 units, 1 becomes obsolete! So... what approach might I take in negotiations with the seller? Does this zoning issue have other significant implications for me as the potential landlord?

I appreciate you all and look forward to any and all thoughts you have to share with me.