When optimizing the navigation of your site it is best to consider the strength of the site at the same time.
If you have a powerful site it is possible that you could put MORE links in the navigation in an effort to expand the reach of your site. Anyone who is dominating their keywords should be able to expand navigation and not contract it - no matter how big it currently is. (If I owned walmart.com I would be comfortable adding more links to the flyout nav - they are getting more powerful in the SERPs. Amazon has been there for ages - they are very hard to defeat in the SERPs - but authority is responsible for much of that and not their linkage IMO)
If you have a weak site that is being defeated everywhere then the best action for you is to get working on the strength of your site. At this point you should have a navigation that makes sense to the visitor.
I cannot figure out how large sites cope with this. As far as I can tell they are using side nav that disappears after selecting a category of item in which the navigation is replaced with filtering tools
I think that they simply have different left navs for different categories and subcategories of the site.
On my sites we solve this with server-side includes... with wordpress you can do it with php... and you can also do it with custom programming that rewrites includes or the nav section of entire websites.
Is there a way to find out exactly what they are doing because I am trying to explain this to our IT person and I just get a response that our site is fine how it is and these navigation links don't affect anything...even though each page starts off with the same 100 follow links of navigation.
lol..... I think that you need to teach your IT person about SEO and your IT person needs to teach you about how websites work. Or... maybe better, I would recommend hiring an SEO to solve both of your knowledge gaps. You both need to know a lot more to run a competitive website.
If you have an IT person who will not accommodate your efforts to improve the SEO of your site then one of you needs to be looking for a new job.