Question about LaCie Rugged Mini

Theoretically yes, via a "release". The following considerations apply: External hard disks are normally connected to a computer (PC/Mac) via USB. If such a hard disk is used for storing data backups, it is "advisable" to do this on ideally several identical hard disks. The 3-2-1 backup strategy says: at least 3 backup generations, on at least 2 different media and one of them is "outsourced" (i.e. offline and deposited in a fire protection zone, ideally in a safe).
Back to the question of simultaneous data backup: As a prerequisite for "sharing", all computers from which such a data backup is to be made must be in the same network (network connection or WiFi required). In the home, the Internet router is one way to set up such a share; this would be recognisable if the router has a USB port. Otherwise, the share would have to be set up as a "home network" on a computer (Google: How to create a home network group). I would organise the data backup using a backup application such as Acronis True Image, Macrium Reflect Free, .... Caution: A backup is only to be considered functional when the data recovery has been successful on a trial basis. If you are backing up data for business purposes, I would advise you to consult a specialist or commission one.

I can't say anything about this, I only use the HD for backing up a single Mac.