Give everyone some time to work on their character - to pad them out with more details about their life - but always building on the base established in previous classes. Where do they work (if they work)? What do they do in their spare time? Are they an extrovert? Do they have lots of friends? Have they had a hard life? Or a life of luxury?
At the party, the groups mingle and try to 'get to know each other' better - by exchanging information about themselves and finding out things about the rest. The group leader can also feel free to leap into the fray at any given moment - to gate crash as an uninvited (or unwelcome!) guest; as the black sheep of the family; as the tedios uncle; the long lost brother etc to spice things up and see how the others react (and interact).
People who live together can choose some kind of domestic context (breakfast the next morning, for example) or they can find a more imaginative setting. People who live alone..... well, they can get gossiping over the garden fence with their neighbour.
Encourage them to share not just the tangible details learnt about their neighbours, but also the feelings and sensations they provoke (do they like them? - in other words - and why or why not?). They can improvise any number of conversations with different combinations of characters and in innumerable contexts.The sky is really the limit....