I think a lot of the replies have made a lot of assumptions about the OP's situation. I'd like to clarify my assumptions (numbered below), and I would be interested in (constructive) feedback, especially from, the OP.
1. He has stated that he is a new investor, but he already has paid off his first investment fully, so he is clearly doing something right. Whether or not he is solely using the rental income to pay off the property or not, he has the ability to pay down a mortgage efficiently.
2. He owns an asset that is worth (low-end) $300k that generates 2300/month (after all costs). He would like to sell it and buy 3 more properties of similar value with 20% down loans. So if he sells, after fees and such, he'll have $270k or so. 20% down on three $300k house = (.20 x 300,00 x 3) = $180K. After buying these new rentals, he will still have about $90k in cash to spend on upgrades and furnishings. That's a lot more than it takes to furnish 3 homes.
3. Financing $240k at 7% will be about $1600 a month in principal and interest. The OP made this math easier for me, since he let us know that he is clearing $2300 a month after all his fees, so that means the only cost he isn't including in that $2300 would be his principal and interest. Subtracting the $1600 leaves $700 of profit with each new house. With three of these houses, he will make $2100 a month, which is comparable to the $2300 he is currently getting.
4. He believes that area where he will be buying the new homes is going to appreciate and attract more MTRenters, but now, the big difference is that he would now have 3 properties that can go up (or potentially down) in value, go up (or down) in rent, and three times as many vacancies to fill.
My back of the napkin assessment is that for only a drop in $200 a month in cash flow, he would control a lot more assets with growth potential and as rents rise over the coming years, the combined rents will increase to a total more than the single rent.
HOWEVER. Selling an existing, well-performing asset has some risks. Why not use the existing HELOC (mentioned in his 2nd post) to use as the 20% down on property #2? 20% of $300k is $60k; financed at 7.5%, that's $420 a month for the HELOC. The profit of the original house would drop by $420 to $1880, but a new property would come under his ownership making $2300 - $1600 = $700. The numbers can be adjusted for taking more from the HELOC to do repairs and add furnishings, but I think it's fair to say that $1880 + $700 - (cost to borrow for repairs and furnishings) will be at or greater than the original $2300 in profit form the single house.
5. Since the OP has paid off the HELOC quickly before, he can do this again. If he uses the HELOC responsibly, he'll be able to serially buy performing hard assets and eventually get to the point where the monthly cash flow will provide future down payments.
6. This is a "me" assumption: I assuming that I made a mistake somewhere in my analysis, so please feel free to show me. :) I learn a lot more from my mistakes than what I (very occasionally) get right on the first pass.