Whether it's okay to switch from "party" to "company" depends on what you mean by these two words. It sounds as if you're using "party" as a group of people gathering together socially, and then switching to "company" as a noun meaning a business enterprise, since you want to use "it". That's not fine.
"company" can mean being with one or more people socially, as in "I enjoyed your company" or "I enjoyed their company." Used in that sense, you don't "join the company," which suggests taking a job.
Look up these two uses in the dictionary and find these meanings.