I suspect you are concerned about not having a 20% down payment because you want to avoid having to pay PMI/private mortgage insurance.
If so, you may be surprised to know that in NY PMI is based on the appraised value and not the purchase price, so if you are buying a home for $460k and you only are able to put $60k down, but for the purchase it appraises for $500k, then you do not have to pay any PMI since $400k loan amount vs. $500k appraised value is 20% equity.
However even if the home doesn't appraise out to give you 20% equity that way, so you have a loan at 86.9% loan-to-value, there are different forms of PMI - including paying a 1 time premium instead of having to pay it on a monthly basis and also taking a little higher interest rate and not having to pay either the 1 time premium nor the monthly payment amount (although the higher interest rate will impact your payments for the entire life of the loan, not just for the period of time you'd have paid the PMI payment for). I don't believe there are any 2nd mortgages going above 80% in the NYC area (which would be the piggyback you are referring to) - but I wouldn't say never.
Everyone has brought something important up though, you said based on the current interest rate environment, and interest rates change all of the time, so if you are anticipating buying 12 months from now, to be on the safe side I'd use interest rates of 1% higher so you don't have to constantly change your plans - and if the interest rates are still this low the closer you get to being ready to buy, you can slowly increase your sales price limit to coincide with the prevailing interest rates at that time.