Why put more money down?

[Val Ault]

Hello BiggerPockets! I’ve been studying everything I can find about Real Estate, and I’m finally getting close to saving enough money for a down payment on my first property, so I’m getting more serious about it!

As I’ve been reading, I’ve started to wonder - when buying an investment property, is there ever a reason to put more money down than the money lender requires? 

For example, if a bank approves me for a loan with 20% down, would there be a situation where I would want to put more than that down? The more money I use in the down payment, the less my cash on cash return will be, and the farther I will be from the down payment for my next property. This seems especially applicable to using an FHA loan to buy a house - if I can just put down 3.5%, is there an advantage to putting down more? (The only one I can think of is that I think there are some kind of monthly fees if you put that little down).

In my mind, it would be better to put as little down as possible and save the rest up as a start on the down payment for your next property. Is that true, or am I missing something?