Being poached to work at the same place under a different company (science research). Advice needed.

I am a researcher on a government research institute on a fixed-term contract and a recruiter recently contacted me about a job on a startup company and started by saying it would be a much higher salary than what I currently make.

This startup is working on a field that has been taking off recently and there are some really big shots behind it, really the top people in Japan in their areas. But this specific job the recruiter is suggesting is extremely niche and probably less than a handful of people in Japan would have more experience than me, so I am in a perfect position to negotiate for the first time in my career. This is also a job I really like doing.

Although it may not seem so bad, since it's basically going from government to industry, the job location is exactly at the same institute where I am currently working, although the startup is on another prefecture. Also I have no idea who is internally responsible for this "collaboration" inside my institute. But I am certain it is not my boss and these internal power struggles can get really messy…

The recruiter probably made a blunder by using my information from 2 years ago, when I was working at a different place. Now that I have this info, I really want to know more about it, and approach it as cautiously as possible as to not burn any bridges.

Ideally I would like to take it as a second job (part time or consulting), since my current work does allow a second job under some circumstances, but I have no idea how to approach this idea with my boss and the recruiter. And since the recruiter payment could be much lower in such case, he may not be happy with the suggestion.

Any advise on how I could proceed? I haven't replied the recruiter yet.

by ImprovementAble8120