amosk,
Thanks for the additional information. There is no "standard policy" that limits tickets AFAIK, so it was helpful to have a few more details to try and determine what the problem is.
The train you're taking is a good choice, as it's direct which means you won't have to deal with a change in Milan. It will have a number of stops however. I did a "test booking" for 23 May, and the Trenitalia website indicates a price of €87 for 3 adults in Economy fare, or €29 PP. However, if I do the same booking with 2 adults, the website shows a total of €38 in Super Economy fare, or €19 PP. It could be that they only have two seats left in Super Economy? Once the quota is sold out for Super Economy, the price moves up to the Economy level.
As today is 24 January, I believe that's now within the 120 day window so you should be able to buy tickets now. You can try to purchase three tickets together on the Captain Train site but if the price doesn't look right, try booking two seats and then one separately. You may be able to choose seats together even if you buy separate tickets (I don't know as I've never tried to book for three people - I normally travel solo). You could also try booking three seats together, but choose the Economy pricing level.
Good luck!