The phrase "a larger majority in" is correct and usable in written English.
It can be used when discussing voting outcomes, opinions, or support levels within a group or population.
Example: "The proposal was accepted by a larger majority in the recent vote, indicating strong support for the initiative."
Alternatives: "a greater majority in" or "an increased majority in".
Voters gave Republicans the House, and then the Senate and a larger majority in the House.
He may be helped by the fact that the Republicans have a larger majority in Congress than last year.
John Major started with a larger majority in the parliament that began in 1992 and had lost it by the time he was done.
With a larger majority in Congress, Democrats are increasingly optimistic that they can realize their dream of affordable health care for all next year.
[New York Post] If the 2010 New York State legislative races took place using the district borders now proposed by the state redistricting task force, Republicans would have a larger majority in the Senate than they do now and Democrats would have a larger majority in the Assembly.
With a larger majority in the Senate, the Bush administration, analysts say, may well be able to win approval for legislation capping medical malpractice payouts, which Democrats have thwarted in the past.
Relations between the government of Prime Minister Recep Tayyip Erdoğan and Turkey's academic establishment have been rocky since Erdoğan's party won a large majority in parliament a decade ago.
Obama had several major advantages over Trump: a high approval rating, a large majority in Congress that was relatively united (including, for a stretch in late 2009, a filibuster-proof Senate), and an economic crisis that created a sense of urgency.
Democrats have a popular president to lead them, a large majority in the House of Representatives and 60 votes in the Senate.
