The Supreme Court agreed Friday to wade into a fight over Congress’ ability to delegate power to federal agencies — opening the next chapter in a decadeslong effort by conservatives and business interests to reduce the power of the federal government.

The Supreme Court could further weaken the power of federal agencies by agreeing to hear a dispute over a Federal Communications Commission program that requires companies to subsidize telecommunications services in under-served areas.

Consumers’ Research, a conservative nonprofit, filed a series of lawsuits claiming Congress violated the nondelegation doctrine by allowing the Federal Communications Commission (FCC) to determine how much telecommunications companies must contribute to ...