"significantly improved on" is correct and usable in written English.
You can use it when you want to indicate an improvement. For example: "We have significantly improved on the customer experience over the last year."
The CBT and CT significantly improved on the global improvement measure and the APT almost reached significance.
Additionally, the quality of the physician– patient interaction, assessed by an experienced performance improvement manager, was significantly improved on scribe visits, and over 5 minutes of extra time in face-to-face interaction with the patient was noted.
Concerned about his cut fastball and changeup after his last start, Martínez said he significantly improved on each.
He averaged 8.1 points a game in his freshman season and never significantly improved on those numbers.
Even while the intifada was raging, Israeli and Palestinian negotiators met in Taba, Egypt, in January 2001, and the Israelis significantly improved on their offer to the Palestinians.
Even the older items were once innovations like my Brown Betty teapot, whose design goes back to the seventeenth century but which is still produced in England, not having been significantly improved on since.
By systematically refining their heuristics, the authors were able to make proposals that significantly improved on their static counterparts.
The mechanistic student groups significantly improved on a proportional reasoning test compared to the calculational student groups.
It's hard to imagine how his bike, which looked more like a tiny landbound rocket than any kind of bicycle, could be significantly improved on.
Work productivity was significantly improved on 4-weeks of treatment by TAPP-CZ nasal spray as compared with placebo.
