In India’s most advanced cities, American companies are racing to set up more and bigger offshore campuses: fully staffed offices with high-skilled Indian professionals, performing functions vital to global business.

The concentration is most stark in bits of Bengaluru. Apul Nahata of RapidAI, a Silicon Valley-based medical technology company that uses artificial intelligence to interpret brain scans, can look out the window of the office he leads in India and see a “density of companies” relevant to his work.