The technique to rank a ‘small’ and a ‘big’ website is basically the same. However, a big website that has built a strong SEO over the years must be treated with care so as not to lose what has been acquired.
The first thing to do is to never drastically change a website. Especially if you change the structure, process ‘in fits and starts’ if possible, in order to be able to test the search engines reaction.
One precaution is essential: for any page movement, do not forget to perform a 301 type redirect so that the robots can find your pages and their ‘history’.
It is possible that your website may lose traffic for 2 or 3 weeks but all your rankings should come back very quickly if you have performed your redirects properly.