More than one Target Market = More than one Brand Promise. Agree?

Most views/definitions of branding take the position that it is the customer who actually determines what the brand means (to them).  Organisations try to influence them.  Hopefully by understanding what their target market wants from a brand.

Thus I have always supposed that any Brand is relative to a particular target market.  Many brands have more than one target market.  This does not become a problem when the TM's are grouped fairly close together of is the brand promise is fairly generic - but what about when two (or more) diverse Target Markets are involved?  It is going to be difficult to offer exactly the same promise/message to them.

So do you have more than one Brand message? What do you think?