It's rare for tornadoes elsewhere, commercially at least.
Some organized chasing efforts have also begun in the Top End of the
Northern Territory and in southeast Australia, with the
biggest successes in November and December. A handful of individuals
are also known to be chasing in other countries, including Israel,
Italy, Spain, France, Belgium, the Netherlands, Finland, Germany,
Switzerland, Bulgaria, Estonia, Argentina, and New Zealand; although
many people trek to the Great Plains of North America from these and
other countries around the world (especially from the United Kingdom).
Overall, Australia seems like your best bet.
It's mostly enthusiasts up north, but they're growing in numbers. A nice report on it is available on ABC, as well as The Age.
Australia Severe Weather is probably your best bet for news on tornadoes and the like there, and The Australian Severe Weather Association would be the one to follow or contact to find out about any commercial groups operating.
There are a few other random Storm Chasing websites in Aus, but they tend to be small individual groups, rather than commercial - however, you might find them keep to take you out for a trip, if you're lucky:
Finally, it's worth noting that most American Storm Chasing companies will keep an eye on the Canadian Prairies, especially during June - as there is the occasional opportunity for it up there, depending on the weather.