Taking a step back, I think various posts are conflating:
- experience with,
- salary banding with,
- company branding
Taking each individually:
- You will have to be able to convince - through past experience and cv - that you can perform at and above the level you want to enter. Anything less and you are asking for a promotion without any proof of ability.
- A lot has been said on the topic of salaries in this forum, but a 40% leap is pretty good anywhere. The fact that new colleagues with less tenure will have similar salaries is irrelevant provided they can perform at this level.
- Posters in many threads are placing way too much emphasis on company brands. It's fine until you're a graduate at the university fair but it's becoming a game of trump cards and over analysed. Company brands will always create reputations, stereotypes and to a lesser degree cultures yet they are ways of filtering and giving some form of expectation to the recruiter, nothing more, nothing less.
A good recruiter will dissect what is real and relevant experience from what is somehow-justifiabily-on-the-cv-but-not really-me.
In conclusion, you may regret it if you pitch yourself too high and eventually may end up feeling undermined by your new team.
That said, you know better than anyone your abilities, achievements and past experience.