KUALA LUMPUR, Malaysia—Investigations into the 1Malaysia Development Bhd. scandal have thus far focused on the alleged involvement of former Prime Minister Najib Razak. But Malaysia’s new government faces an awkward problem: How far should it pursue the companies that played a supporting role in one of the world’s largest-ever financial swindles?

Since Mr. Najib was forced out of office in an election upset, succeeded by veteran premier Mahathir Mohamad, the extent of the alleged theft from 1MDB has faced renewed scrutiny....