President Donald Trump’s clash with Silicon Valley over immigration is about to become even more contentious.

After the new president banned refugees and travelers from seven predominantly Muslim countries, Google, Facebook, Salesforce, Microsoft and others railed against the move, saying it violated the country’s principles and risked disrupting its engine of innovation. Trump’s next steps could strike even closer to home: His administration has drafted an executive order aimed at overhauling the work-visa programs technology companies depend on to hire tens of thousands of employees each year.

If implemented, the reforms could shift the way American companies like Microsoft Corp., Amazon.com Inc. and Apple Inc. recruit talent and force wholesale changes at Indian companies such as Infosys Ltd. and Wipro Ltd. Businesses would have to try to hire American first and if they recruit foreign workers, priority would be given to the most highly paid.

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