How to Update Look-Alike List in Clay and Avoid Duplicate Companies?

I have a look a like list that I created in Clay and I only initially pulled in 1k companies into the list initially. Now the table has a bunch of enrichments to find the right contacts, write the email, etc. I would like to pull new companies into the table if possible or be able to create the same look a like search that does not pull in the same companies again. Is this possible? Or should I do the same LaL search, suppress out the companies and rebuild the table?