"far greater implications" is a correct and usable phrase in written English.
You can use it when you want to emphasize that an outcome or situation has far-reaching effects or implications, often of a serious nature. Example: The discovery of this new technology has far greater implications than we could have ever imagined.
"What happened at The Oval... has got far greater implications than it apparently looks," the sports secretary Ashraf Khan was quoted as saying.
George Bush, who swept into office on a cloud of moral umbrage, now has his own sex scandal -- one with far greater implications than titillating cigar jokes.
Not so long ago, there were real fears that Spain could turn into the next Greece – with far greater implications for the euro and EU economy because of its greater size.
By his account, it wasn't just about the money: the blockchain that ledger of permanently documented exchanges, which is distributed by participants in a given protocol's network has far greater implications.
But the observant Internet connoisseurs of Reddit uncovered something with far greater implications: Robin Thicke is actually a human Ken doll.
Citing that religious freedom is an issue that has "far greater implications for America's future", he said that "today, at the city, the state, and the federal levels, government bureaucrats are daily trying to limit that freedom, impose restrictions, and stifle expressions of faith on campuses, in hospitals, and in businesses".
This issue, I believe, has a far greater implication than whatever problems the GOP may be causing for itself at the level of how its members talk about women, cultural diversity, and religion.
But suffice to say there are likely to be far greater and deeper implications to this deal than we have heard about so far.
When, midway through, Marceline's tattooed number is revealed, the sudden arrival of the subject of the Holocaust carries a dramatic weight — as well as a power of implication — far greater than if it had been announced from the start.
But the implications are far greater than the mere issue of teachers' health plans.
This crisis is not just a humanitarian disaster; the implications are far greater.
