For many years we have offered social support set up in the format you are thinking of, Angela. We use volunteers we have trained who coordinate and meet with the bereaved via a Men's Breakfast, a Ladies' Lunch, and we are revamping our evening "Night Out" program. We publicize these in our newsletter and remind people of this option at our groups. When we find support group attendees are no longer attending for grief related reasons but more so for social ones we follow up with them after group to talk about that. We encourage them to conisider taking a break and maybe then taking some training to be a volunteer themselves or suggesting they instead attend our more socially focused options.
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The research literature confirms that most people heal on their own, drawing from their own social support networks and many who do reach out to us for support need very little - sometimes only needing to attend 1-2 groups or individual sessions. It's a small segment of the larger population who need much in the way of groups, far more cope and adjust well with just social support.