Can I be denied transport if train is full?

[Rpita]

Hello!  I am traveling from Milano to Domodosolla on September 19.  The morning trains from Milano Centrale were all sold out so I switched to Milano Porta Garibaldi.  It appears the trains from Domodosolla run hourly to Brig.  I have a Swiss Travel Pass.  Is there any chance the train will be full and I will not get the time I want?  I do currently have the option of buying full fare ticket but don't know if that is necessary.  Thanks for your help!

[Rpita]

After rereading my post I realize it is a bit confusing.  My question is:  if all the trains coming from Milano to Domodosolla are full, will people stay on and no seats will become available?  I am considering buying a second class ticket from Domodosolla to Brig instead of using my 1st class Swiss Travel Pass.  No sure how all this works but I need a particular time to leave Brig in order to meet up with friends.  Thanks!

[FatimaH]

Hello @Rpita 

From Domodossola to Switzerland or from Switzerland to Domodossola, seat reservation is not mandatory. You can usually travel without a seat. If the train is very crowded, passengers without a seat reservation may be asked to get off and travel on a regional train. From Domodossola to Brig you do not need an additional train ticket if you have the Swiss Travel Pass.

I wish you a nice day.

Kind regards,
FatimaH