Cash out refinance my current house to buy my next house?

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Hey there! First time posting newbie here. I am entirely new to the real estate industry as a means of wealth. I recently accepted a position as a CFO of a property management company. I have extensive experience running a company as a 28 year old, and this will be a big new one. I only say this because when I was looking at this position, my mind was blown on the benefits of real estate investing through rental properties. BLOWN! Anyways, that rant is over. My current situation: I bought my current house (3 bed 2.5 Bath 1790 SF in Tennessee) in 2014 on a 15 year note ($~1280/mo) with 151k financed. I owe $116k more (current estimated value $270k). My son is reaching the school age so I am looking to buy a house in the preferred school district. The house I am wanting to get is somewhat larger, 4 bed, 3 bath with estimated cost 330-350k. Savings wise, my situation isn’t the best. $10k liquid in the bank. IRAs have about $20k between my wife and I. Then a whole life insurance plan that is $20k cash between my wife and I. My new job once I start will start up my savings once again. Basically the decision I’m fighting with in my head is 2 paths to buy my new house and keep my current: 1- save up as much as I can from new job. Best case 10-12k more over the next 12 months. Then buy my next house with that cash which won’t amount to a significant down payment. And leave all equity in my house alone. 2- save this same cash still, BUT cash out refinance my current house to leverage 75% of my house which will be 90k give or take depending when this happen. My thoughts: 1- not much to think about as I’m not doing anything other than saving so I’m not leveraging my house’s value to expedite my purchase(s). Not a huge fan. 2- all the thoughts! With this 90k I can buy my new house and save the difference or buy another 2-3 potentially. Being that I am going to be working for a property management company, I will learn a lot about that side of things so if the cash flow doesn’t allow for that management, I can bootstrap that. My BIGGEST concern with this is taking away my 3.5% 15 year note. Even though, realistically speaking, if I refi my house for a 30 year total 206k between current mortgage and cash out the payment will be very similar, cash flow won’t change much. My house will also rent for 1795/month based on comps in the area. Only a 5 year old house. Apologies for the long tail a story I just gave you! I would appreciate any and all input!

@Patrick Leitch , by refinancing you will also restart your amortization schedule + likely get a higher rate. Leave your note alone, get a heloc to buy a next house, pay heloc off with rental income / savings, repeat the process once you are ready for another investment property. Good luck