Hi,
HikaShop have a Joomfish/Falang integration that allow to create translations for every HikaShop elements (products, categories, order status, etc).
After that, you can use the multilanguage Joomla system but your products would just stored in one language.
Our demo website use Falang, you can take a look of the integration.
After that, it is not possible to have several languages in the same time. But you can use same translations for several languages in order to have the same result.
Regards,