Yes, in principle. This is why, when you file your own application, you should file in as many different Classes as are necessary to cover all the different products or services you currently provide or which you intend to provide. A manufacturer of various different products should make sure that all such products are covered by claiming protection in the appropriate Class.
Posted in: FAQ Page
If I have registered my name for one kind of product or service can someone else register it for a different kind of product or service?