If I put 60% down on a purchase, can I still get a loan against the property for the remaining 40%?

Generally yes. A loan for the remaining 40% is about as conservative as mortgages get from a lender's standpoint. That said, "generally" is doing some work, because several variables can turn it into a no in specific situations: the property's location and type, the purchase price, your credit, and your ability to document income all factor in. Property type is the common sticking point. On a very low-priced or unusual property (say a $60,000 tiny home), a lender might decline to make the roughly $25,000 loan at all, because the loan is too small or the collateral too unconventional to fit standard programs, regardless of how strong the rest of the file looks. The honest answer: the large-down-payment, small-loan structure is rarely the obstacle. What matters is whether the specific property and borrower fit a lender's guidelines. Tell us the property type and price, and we can tell you quickly whether it's financeable.