Increase your existing mortgage
You could try approaching your existing mortgage lender and asking if they’re prepared to lend you more money. You might do this if your existing mortgage deal has low interest rates (and you’d like to stick with your current provider). You may also want to do this if you have significant penalties for terminating your existing mortgage, which outweighs the benefit of remortgaging.
However, as with remortgaging, any such advance would be secured against your home, and you would still need to pay back the extra money. Also, be aware that the interest rate you’re charged on the additional borrowing could be different to your existing mortgage rate.