Even after the real estate crash, there are banks that lend money outside of the rules I'll share.

A fully qualified mortgage is typically run at debt to income ratios of 28/36, where 28% of your gross monthly income can apply to the mortgage, property tax, and insurance, and the 36% is the total monthly debt (including the mortgage, etc) plus car loan student loan, etc. It's less about the total loan on the potential than about these ratios. The bank may allow for 75% of monthly rent so until rentals are running at a profit, they may seem a loss, even while just breaking even. This is just an overview, each bank may vary a bit.

There's a couple issues to consider:

Capital Gain Exclusion

When you sell your primary home, the IRS gives you a $500k exemption (married, filing jointly) on gain. If you decide not to sell your current house now, and you subsequently fall outside the ownership/use tests, then you may owe taxes on any gains when you sell the house.

Debt/Income Ratios

Rather than being concerned about your net debt, you should be concerned about your monthly debt payments. Generally speaking, you cannot have debt payments of more than 36% of your monthly income. If you can secure a renter for your current property, then you may be able to reach this ratio for your next (third) property.

Also, only 75% of your expected monthly rental income is considered for calculating your 36% number.

Risks

(This is not an exhaustive list of risks you expose yourself to).

The largest risk is if you or your spouse find yourself without income (e.g. lost job, accident/injury, no renter), then you may be hurting to make your monthly debt payments. You will need to be confident that you can pay all your debts. A good rule that I hear is having the ability to pay 6 months worth of debt. This may not necessarily mean having 6 months worth of cash on hand, but access to that money through personal lines of credit, borrowing against assets, selling stocks/investments, etc.

You also want to make sure that your insurance policies fully cover you in the event that a tenant sues you, damages property, etc. You also don't want to face a situation where you are sued because of discrimination. Hiring a property management company to take care of these things may be a good peace-of-mind.

We have never had a problem securing a new mortgage while still owning the home we were in... whether we said we intended to rent it or sell it after we closed on & moved into our new house.

We are not particularly wealthy— upper middle class— and are in the process of purchasing a new home, & expect to close in about 1 month. We pre-qualified for a loan that is easily $150k over what we would ever spend...

Prior to this, we kept the homes we had because they were in areas where nice rentals were in high demand. The house we are currently living in, we will sell because it has a lot of property around which requires a great deal of upkeep. This makes it a less than ideal to find tenants who would do the amount of work needed. Nevertheless the mortgage company was fine with us not selling that house prior to purchasing the new one.

We own 5 houses/properties with a combined total worth of ~1.8M— although we owe much less than that— perhaps 50%, or perhaps slightly more. (I don’t have the numbers in front of me & am not inclined to look them up at this time.) 4 of the 5 are generating income of about 15-20% above the mortgage payment.

I certainly didn’t think we’d be able to put an offer & purchase another $500+k home without having the contract be contingent on the sale of the one we’re in. But apparently, if the market is brisk, and you have an excellent mortgage history... the lender will be more inclined to make allowances— at least according to our loan officer.

Of course, ymmv. The only person who can give you an accurate answer based on your circumstances, is a loan officer familiar with your situation.

Good luck!