User/Searcher Personas
At this point, you may not have your own searcher persona built, but many businesses have already gone through a process of creating ideal customer profiles. Looking at these customers alone can help you generate new keyword ideas. You can also check the list of keywords you generate through the persona profile trait set to see if they are actually relevant to the terms that will drive traffic from the users your site is trying to target.
Consider this example of an electronics company, which has created a persona/avatar for its ideal customer. While the site sells a wide range of computer and electronic components and cables, it's helpful to know that its ideal customer isn't your average B2C user looking for a cable for their Blu-ray player. Instead, it's a B2B IT professional who deals with electronics for Fortune 500-sized companies.
This information allows me to not only filter out search queries that are clearly consumer-based or looking for individual units, but also filter out informational queries. For this customer, the search query from my initial list, "what topology uses the least amount of cabling," may be relevant, but "what cable do I need for ps4 controller" is not.
Current keyword lists
If you have a new project, with someone who has compiled a list of keywords for the site before, and the list is available, starting with that list as a basis for new keyword research should be a good starting point. Unless the nature of the site has changed radically since the research was done.