Yes it is possible.
Each origin as the Cutoff_,attribute name> property that can be set. So if you are solving on a length attribute in miles called Length, then the origins attribute table has a field called Cutoff_Length. You can set it individually for each origin. Or better yet, when you do a Load Locations, this property is listed, so simply map it some field on your existing origins point feature class and have it loaded with the origin locations.
Similarly the facilities on the service area solver have a Break_<attribute name> property. You can set it how big of a service area you want computed. And again, you can use Load Locations to load it as well.
Regards,
Jay Sandhu