Three websites means:
- 3 times the link building
- 3 times the content writing
- 3 times the monitoring
Three websites do sound tempting until you realize that you will not be able to benefit from each area driving its own links. With a single website you will be able to receive the domain benefit for every link you generate, while having multiple domains you will not.
Another problem with linking to other websites all the time is the drop in link juice. While it may seem beneficial to pass links from your websites, you have to remember that you are giving away some of the value of your internal links each time. With just a couple links its no problem, but with dozens you might face a dilemma.
I would stick to the one website with landing pages for each area of interest. I would then do an intense link building campaign for each, and write a very informative blog (to both drive visitors and links). By having high quality landing pages for each "department" you will be able to achieve all your SERP goals, and be able to build on each "departments" success.
The only reason I wouldn't do this is if I was going to have 1000's of pages of content for each department.