"together discover" is a correct and usable phrase in written English.
You can use it when talking about two or more people who are collaborating to uncover something. For example: "The researchers worked together to discover a new, innovative approach to cancer treatments."
We used to watch TV together, discovering who shot J R and talking about it the next day.
Had they, together, discovered the excitement of a shadowland and kept it alive in the bluster of daring and pretense?
The teams together discovered the cause of the die-offs, a previously unknown pathogen species now named Phytophthora ramorum.
Later they resurrected the music of Vivaldi together, discovering manuscript scores of his concertos in a Turin library.
The mansion's current incarnation began three years ago when Mr. Shapiro and a few friends who wanted to live together discovered the building and recognized its possibilities.
At university she joins a sorority; in the sorority house the girls are busy becoming women together, discovering themselves and other people, becoming "sisters".
Still, they kept working together, discovering a shared sense of very dry, oddball humour that percolates throughout their oeuvre, from track titles to album sleeves to videos: "It's not like we say 'we've got to do some humour, people will like this'," notes Blank, "it's just what happens when both of us are around together".
Ms. Hesser, a former New York Times food editor, and Ms. Stubbs, who has also written for The Times, collaborated on "The Essential New York Times Cookbook" and other projects, but together discovered that their favorite dishes were often those they learned about from home cooks.
In an article also appearing in today's Nature, David Jewitt of the University of Hawaii and Jane Luu of the Lincoln Laboratory at the Massachusetts Institute of Technology, who together discovered the first Kuiper Belt Object in 1992, report the presence of crystalline water ice on the largest known Kuiper Belt Object, Quaoar (pronounced KWAH-war).
