Front also rolled out support for "accounts" last year which sounds exactly like what you are trying to do. It aggregates a set of contacts under an account and lets you use accounts through the whole application.

You can see all of the communication from a company across all channels (support, sales, success), get automatically notified if someone else in the organization replied recently, do routing/classification based on account data (account size, account owners), and filter analytics by account.

Worth a look if you're considering going off Helpscout.