As a coach over groups in my local church, I spend a great deal of time thinking about and praying for the groups I oversee. I'm always asking the Lord what I might be able to do for the group to encourage it to keep reaching out to unchurched people and consider multiplying sooner than later.
Here's a few things I'm doing that seem to work well in my situation:
1. I pray with the leaders of the groups often, asking them to pray with me and ask God to bless them with a large group that will require a multiplication.
2. I encourage the group's core team (5-8 people who get together monthly to make plans with the leader) to meet consistently in a host home where a group might multiply, not in just one home. If people become familiar with a new host home, they're far more likely to be open to meeting as a new group in that home.
3. I ask the worship leader of the group to train someone to lead and share the worship time with them 50/50 until the group multiplies.
4. I ask the existing leader of the group to ask one of the core team members to facilitate the core team meetings in the future. This turns a core team member into a group leader naturally, and gives the leader a break.
5. I visit the group and ask them if they've achieve all God wanted them to achieve. I ask, "Are you done? Or, is there more to do as a group beyond loving one another, which you're already doing beautifully?" This forces them to think of God and others aside from themselves.
Coaching groups in this way is weak in American churches with small group ministries. The coaches make a phone call to check in with the leader once a month at best and they're typically given far too many groups to support.
I'd love to see what your church's coaches are doing that gives results (versus what you want them to do or they're supposed to be doing but not doing... which has a simple solution: modeling.)