Could I just refill the carbonation canister?

You may do this, however, the CO2 in the sodastream tanks is FDA certified as beverage grade carbonation. Local businesses may not have this level of CO2 to refill you tank, this potentially leads to toxins being introduced into the CO2. Having the canister refilled could cause damage to the carbonator, which sodastream will not repair or replace. For the sake of our machine, it is better just to buy a new CO2 canister each time.

There are online stores who sell devices to help do this.

I DO NOT work for any of them.

I bought a device to connect a regular Co2 tank to my SoadStream.

I now use a 5 Lb Co2 tank that

I bought at a Home Brew shop and pay about $15 to have it refilled.

As for refilling the original carbonation canister,

beware of the valve in the top. It can make refilling difficult.

Look around the web, there are less expensive solutions than $15

for a 14.5 oz of Co2