If you drop that central motivation, but don't make any other adjustments the problem is how to keep the campaign together as a group game. You need to figure out why these characters would stay together for an extended period of time if they don't have any goals other than gathering resources for themselves. Probably the simplest example of an externally motivated campaign is that the characters are physically isolated in a location where their only option is to work together, like a small town surrounded by wilderness. (i.e., The Keep on the Borderlands, an oldie but goodie). They could be isolated in some other way for example, the only dwarves in a human kingdom. Or they could have something in common that binds them together - family ties, on the run from the same archmage, employees of the same trade guild..
