You are referring to the Swiss Travel Pass for tourists, right? Not to confuse, as the Swiss Pass is a resident product.
Swiss Travel Pass – the All-in-one-Ticket for Switzerland | SBB
Yes, you can buy tickets using one mobile phone, you simply have to add all other passengers as co-travelers: SBB Mobile: your personal travel companion | SBB
Are all family members above 16 years of age? For children (6-15.99), there is the Swiss Family Card; with it, you do not have to buy tickets when the children are travelling with you while you hold the Swiss Travel Pass or any other valid ticket.
Swiss Family Card | Switzerland Tourism (myswitzerland.com)