The phrase "an increasing possibility" is correct and usable in written English.
You can use it when discussing the likelihood of an event or situation becoming more probable over time.
Example: "With the recent changes in climate patterns, there is an increasing possibility of severe weather events occurring more frequently."
Alternatives: "a growing likelihood" or "a rising chance".
An economic slowdown is an increasing possibility.
An oil spill is also an increasing possibility as traffic through the tight coastal channels escalates.
If a mutual parting of the ways this summer appears an increasing possibility, there seems little boardroom appetite for making an imminent change.
Rethinking Replay There is an increasing possibility that instant replay might not be approved by the owners when they gather for their annual meetings this month.
Spending years in jail instead of prison is an increasing possibility now, as California carries out the most far-reaching overhaul of its criminal justice system in decades.
Driving the networks' online efforts are the opportunities to reach viewers who might not otherwise turn on a television on election night (an increasing possibility, as television news viewership falls each year) and to offer them new, often interactive technologies that are simply not available through a traditional cable box.
If only partial necrosis is achieved, future re-treatment may be necessary, which may result in increased patient discomfort, greater technical difficulties, higher failure rates and an increased possibility of complications.
The Clinton administration recently deferred to China's opposition to such sales to avoid an increased possibility of armed conflict.
Men also correlate youth with health and hence with an increased possibility that their spouse will have healthy children.
"Recent weather patterns suggest an increased possibility of freezing cold air from Russia pushing right across west Europe and the UK during January.
A credit rating downgrade is now very likely and a hard landing for the economy is an increased possibility as consumers and business react cautiously to the political impasse.
