One of my clients has the same problem, so I looked at some of the biggest websites within the industry, and they also share the same issue and have more than 200 internal links on their homepage and the majority of their internal pages.
I would say that it wouldn't have a massive impact upon your rankings or PA if you were to reduce the amount of internal links, but you could use the nofollow tag tactically to do so. For example: if you have a link to a page within your top navigation, you could nofollow a link to the same page if it's also featured within your footer or sidebar.
This is just an example. I wouldn't recommend doing this, but it's an easy way around the problem if you're keen to resolve it and it won't have an impact upon usability.