Just closed on 1st investment using conventional, can i purchase 2nd right away?

[Michell Chase]

I am currently retired and just purchased my 1st duplex in Upstate NY using a conventional investment property loan.  I am interested in purchasing a 2nd multi family right away while the market is good in that area.  Everything I have read says I wouldn't get a 2nd conventional loan right away even though my numbers are excellent (credit above 800 and over $500k in my 401k with a monthly pension).  Should I consider private lending to purchase a 2nd multi family right away as to not lose the opportunity?  (130-150k range). ( I do not live in NY so primary residence loans would not apply).