Can a dealer get a vehicle from another make?

I have been going online recently, have seen the triumph daytona 675, and would like to look at and (probably) buy one, however the shop in town is a honda motorcycles, will they be able to source a bike from another make or are they stuck with new hondas?

(the nearest triumph dealer is a good 2-3 hours drive away)

Franchise agreements by brand and state warranty laws, bonding, licensing mean a new 'other brand' is highly unlikely. Local dealer that has a established relationship with the other dealer as in swapping tradeins of the other dealers line might get a reasonable deal on the 'other line' model- if the Honda dealer has been sending used tradein Triumphs to that dealer, he has been sending Honda's to the local dealer then a maybe year or 2 old Triumph might be available as a 'accomidation' to your local dealer and possible warrantee for say 30 days or so. Depends a lot on the relationship between the dealers- BMW and Harley dealers sometimes have old aquaintence and trading- locally the Beaver Dam dealer was both BMW and Harley, did arrangements between both other Harley and BMW dealers. Otherwise be prepared to travel. I used to work at a Jeep and Renault dealer in parts room- had working deals with the Fiat and BMC/Austin parts guys for discount on parts for their brands taken in trade or local customer travel restricted- we split wholesale parts discount and made money on service rate for our 'off' brands and warrantie paperwork was as if 'city' contracted for parts.

Not a new Triumph. Those are only sold by Triumph dealerships.

The Honda dealership might take a Triumph on trade, but they can't get you a new one. You will have to go to the dealership 2-3 hours away.

You will need to travel 2-3 hours to buy parts or get it serviced why not travel that distance before you part with your money because you can bet that your local dealer will charge you (in their price) for resourcing and collecting the bike (even if they are permitted to do it under their franchise agreement).

Yes.
Dealers buy from other shops when their inventory runs out.
But that is same brand shops.

Cross brand (Honda - Triumph) will cost you.
It's as if your dealer were to buy a car and sell it to you.
They will want to make a profit after buying the vehicle at retail price from another dealer.

You will not get a warranty for your new Triumph.
I don't think warranties are transferable to second owners.

Rethink your purchase choice.
You will have to travel 2-3 hours to get your new bike serviced.

They wouldn't be able to get a brand new one from Triumph but they may be able to get a demo or used model from another dealer.