Increasing cost basis to pay less tax?

Let’s say I bought a lot of shares of a stock that has since increased by a large amount. Would it be beneficial for me to buy additional shares while the stock price has increased in order to increase my cost basis, which in turn allows me to pay less taxes by reducing my capital gains? Or is it better to keep my cost basis low to have more of a profit?

Sorry for the wordy question but it has been something that I have been wondering. Any advice is appreciated.