The phrase "be highly influential on" is correct and usable in written English.
You can use it to describe the impact of someone or something on a particular situation or process. For example, "The new legislation is expected to be highly influential on the development of the housing market."
The distance of the reinforcement to the neutral axis was shown to be highly influential on the mechanical enhancements.
Although veterinarians provide advice and support to smallholders, only 14.5% considered themselves to be highly influential on smallholder practices.
How the governments vying to become new financial services hubs for China in Europe negotiate with China will be highly influential on the outcome.
Trust may be highly influential on perceptions of emotionally charged scientific issues (Dunn and Schweitzer 2005; Romano 2003) such as food that includes genetically modified organisms (Broughton and Nadelson 2012), climate change (Dunlap and McCright 2011), vaccines (Keelan et al. 2010), and potentially with biological evolution (Smith, et al. 1995).
Their later work, almost all of it outside of Scotland, would be highly influential on an international scale.
This sound, and lead singer David Lee Roth's stage antics, would be highly influential on glam metal, although Van Halen would never fully adopt a glam aesthetic.
It's always better to think more holistically because all these elements of well-being are highly influential on others".
Country guidance issued by the Home Office is highly influential on both ministry officials and judges making decisions on asylum claims.
The immediate tissue microenvironment of implanted biomedical devices and engineered tissues is highly influential on their long term fate and efficacy.
