Do second mortgages work this way?

I’m looking into doing my first house flip and I’m trying to figure out how to finance it. This is what I was thinking about doing, but I’m not quite sure if this makes sense, or if it is allowed. I have no money to put down on the investment property. I only have the cash to cover closing costs. I was thinking of taking out a first mortgage for 80% of the purchase price and taking out a second mortgage for the remaining 20% plus estimated home renovation costs. For example: I buy a house for $ 100,000. I take out a first mortgage for 80% ($ 80,000). Then I take out a second mortgage for 20% ($ 20,000) plus an extra $ 20,000 for renovation costs. So the second mortgage would be for $ 40,000. Do second mortgages work this way or would the bank reject my request for the second mortgage for some reason?

I primarily would like an answer to this question specifically, but it would also be great to get suggestions on other, better ways to finance a house flipping project if I have no money for a down payment. Thank you in advance!

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