Mixing species of animals can be very dangerous. Mixing rodents with other rodents is unnaceptable. A dog that has never been exposed to small animals might attack, cats... I don't really trust them even if they have been socialized with small animals (not saying here that you can't keep rodents and cats... just saying don't let them play together, and keep cat away from rodent cage room).
In other words... no... syrian hamster, alone.... dwarf hamster, with another dwarf, if they have been propperly introduced.