Hey Naomi,

seems the train is sold out (at least not enough space for 4 persons):

Will take longer, but: you can take instead a regional train to Domodossola and from there another regional train to Spiez (if you have enough time, stay on the regional train in Brig - more scenic). 
Advantage: Saves you 44 euro!

The Route with the regional train from Domodossola to Spiez is stunning especially as @MartinM  said after Brig be sure to have seats on the leftside in direction of travel :D

Thanks for the info!the train chosen, however, would be that of 07:20 AM from central Milan and it would seem that there are still seats (I sent a request to the SBB chat which confirmed the availability of seats but they cannot make the reservation)

Sorry! My mistake. I checked it while phoning at work and choose the wrong connection!

indeed there would be seats available for the train at 7.20. are you in Italy right now? Then go to a ticket office and buy the reservation there.

Thank you very much!

Hi, there is currently an issue on our side that does not allow seat reservations to be booked for more than one traveller. As a workaround, you can go to your account → trips & travellers, and add travellers or (if already done so) complete the missing information of the travellers. More information can be found here. You should now be able to book through our system, but you can also choose one of the alternatives mentioned.