When Donald J. Trump started his first campaign for the presidency, two Trump-branded buildings were going up in India, one in the financial capital of Mumbai and the other nearby in Pune. Before he won in 2016, the Trump Organization expanded its business in India, signing deals in two more big cities.

       The day after Mr. Trump’s victory in November, a developer in India told local media about half a dozen new deals. Like the others, Indian companies buy the land, build the high-rises, sell the units and pay a fee to use the Trump name.

       These deals are putting India even more squarely in the Trump Organization’s sights. And with Mr. Trump on his way back to the White House, the country is emerging as center stage for potential conflicts of interest.

       In Mr. Trump’s first term, it was uncharted territory for a sitting U.S. president to have extensive business interests in foreign countries. During his second term, the Trump Organization aims to issue a more limited ethics plan that is unlikely to significantly curb its growth.

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       The United States remains at the heart of the Trump family’s real estate business. Elsewhere, there is one Trump Tower each in the Philippines, Turkey and Uruguay, and the company has struck deals to bring Trump Towers to Saudi Arabia and the United Arab Emirates.

       But India stands out: The Trump company’s business partners here have plans to bring the total number of Trump-branded buildings to 10 in the coming years.

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