WASHINGTON—The Trump White House, confident that its hard-line strategy is succeeding, is planning to ratchet up the pressure on China by focusing on new tariffs and threatening to block Chinese technology investment in the U.S., according to officials familiar with the strategy.

The additional moves come as President Donald Trump has told his senior aides to investigate the possibility of joining the Trans-Pacific Partnership, a move that would reverse a Trump campaign promise and further challenge China, which isn’t part...