The phrase "a much larger majority" is correct and usable in written English.
It can be used when discussing a significant increase in the proportion of a group that supports a particular idea or decision.
Example: "In the recent vote, a much larger majority favored the new policy compared to the last election."
Alternatives: "a significantly greater majority" or "a considerably larger majority".
Better, so goes an argument popular with Tory MPs, for Mrs May to armour herself with the much larger majority that the opinion polls indicate can be hers for the asking.
A Fast Company profile reporting that the team wants to "make mom and pop corner store's obsolete," understandably aggravated many who are already worried about the growing wealth disparity between the "haves" in tech and the much larger majority of "have-nots".
Come to think of it, the Republican House and Senate leaders now bemoaning the legislative activities of a much larger Democratic majority were only to happy to press their advantage when they had it.
National polls show huge majorities favor keeping Medicare and Social Security in something approaching their current form — much larger majorities, tellingly, than oppose an increase in the debt ceiling.
Any fresh injection of government money, or the conversion of its existing preferred shares into common stock, would give taxpayers a much larger — perhaps even a majority stake — in the company.
Our study included a much larger sample, and a majority of short-term survivors, in contrast to Avis, et. al.'s inclusion of only long-term survivors.
They created an autonomous zone outside Baghdad's control and since the US invasion have had autonomy through the Kurdistan Regional Government, but they control a much larger area where Kurds are the majority – this is the area now disputed.
Another hashtag arose, #StopGamerGate2014, and with it a much larger volume of tweeters (the silent majority that gaters presumed were on their side) and responders moved to anger.
They created an autonomous zone outside Baghdad's control and since the US invasion have had autonomy through the Kurdistan Regional Government, but they control a much larger area where Kurds are the majority - this is the area now disputed.
