One option would be to use the equity I have in my current house towards the purchase of a second house.

Not exactly, you could use the land as a down payment to pay for construction of a new house on that land; However, to get money out of that land without selling it to buy a house somewhere else, you'd have to take a loan against that land and the bank financing your new mortgage won't like that at all and is not really an option. (This is USA-centric advice)

Edit: for context I went through this process (for my first place I don't own two places) and when you go to get your second home, the first question the bank will ask you is where the money came from for the down payment - if it's from a loan or a gift they will pretty much shut you down right there. A lot of this stems from the '08 crash.

If you take a loan with your first real estate as collateral, you might lose it if you aren’t able to pay the loan. So in the worst case you lose the old and the new property, if you run into cash flow problems.

Taking out a loan to buy a second property can pay for itself, if you do it right and aren’t unlucky. Live in your old house, take out a loan to buy a second house. Rent out the second property and pay the mortgage with that income.

Owning two properties means you have administrative costs and time you need to put in.