How firm is the 2-years of income rule for self-employed people?

[Svend W.]

Hi folks

I'm interested in pursing REI opportunities in small multifamily, but recently switched from W2 employment to self-employment.

My impression is that the rule of thumb here is that banks want to see 2 years of 1099 wages before lending to self-employed professionals. 

Is there any flexibility on this if someone has excellent credit and/or is ready to put down some collateral? 

If so, do you recommend any particular banks? I'm in Chicago.

Thank in advance.