Seems like something an A/B testing tool could be modified to do, if you could get the data from LinkedIn via an API or something and show a certain 'variation' based on which the user matches a certain category/number of categories.

However, it seems like something that'd take an awful lot of work, and the amount needed would basically grow exponentially depending on how fine grained you wanted the targeting to be. That probably wouldn't give you a great return on investment, especially given that even a perfectly targeted website is nowhere near sufficient enough to guarantee a sale/make it that much more likely.