How to setup simultaneous outbound faxes?

Basically, every user extension under your account (company) will share the same fax number (which usually is your main company number). Thus, every fax sending out thru the same number will be on the same queue.

For your use case, I suggest that you should add more phone numbers (let's say 3 more plus the current main company number to match your 4 lines). Then you should create 4 dedicated extensions (let's name them "Fax station 1", "Fax station 2" etc.. Each "Fax station" extension will be assigned with a different fax number.

Set Fax settings for each extension

Select Fax number for each extension

Now it's up to you to implement your fax app to select a "Fax Station" extension to send out a fax. You can query fax messages status of each "Fax Station" to see how many faxes are on the queue of that fax station and decide which one you want to use for sending a new fax.