TPG is aiming for a valuation of as much as $9.3 billion in its U.S. initial public offering, as the private equity powerhouse finally moves closer to a stock market flotation after toying with the idea of going public for several years. The firm, an investor in Airbnb Inc., Uber Technologies Inc., and Spotify Technology SA, said on Tuesday it planned to sell about 28.3 million shares priced between $28 and $31 apiece in the offering. TPG would raise about $877.6 million at the top end of the range. Its existing investors plan to sell roughly 5.59 million shares, the proceeds from which will not go to the firm. The buyout giant, among the last major players in the industry to remain in a closely held partnership, has made its approach to go public several years after rivals such as Apollo Global Management Inc., KKR & Co Inc., and Blackstone …