Christian organizations generally don't partner well with other organizations.*
Here are three basic principles that should apply to Christian organizations as well as Christian individuals:
1) God gets all the credit, and He has all the control, not me or my organization! This means I don't ever get to enter the partnership looking to "get what I want," or "get what we need." It also means I don't get the credit for it. We partner around what God is doing, and all organizations in the partnership need to prioritize His work, not ours.
2) If we belong to Christ, then we belong to each other! This means I cannot claim that my organization is independent of the Church as a whole. I may not ignore other Christian organizations in our world, just like I must not ignore other Christians in my church.
3) The Church exists for the sake of the world, not its own sake! We are called to serve others, not ourselves. We must prioritize the shalom/salvation/blessing of the community we live in, not our own.
If we were to follow these principles, we would partner more often, and with greater health and effectiveness. Where multiple organizations are working together to bless the world around them because of their common Christian identity, and eschewing credit and control, there you will find power, glory, peace, and joy spilling into our communities.
However, there would be countless situations where we wouldn't partner as well. We partner around what God is doing. There are Christian organizations that we don't partner with because they are called to different parts of the Kingdom work, or different parts of the world. The knee and the elbow are both part of the same body, but they don't touch each other directly. This means we should not feel obligated to partner simply for partnerships sake, but again, because we are prioritizing God's agenda and God's action.
What organizations are operating in the same geography as yours? What organizations are working on the same issues as yours? What organizations do you have relational connections with?
How could your organization partner around your mission with some of those other organizations?
*Secular organizations aren't any better at this than us. There is a large secular organization in our neighborhood who has a long track record of helping the neighborhood, but they run roughshod over other neighborhood organizations in the process. The root causes are the same, an arrogant myopia about their wisdom and skill, and conflating institutional maintenance with institutional mission. This behavior doesn't help the neighborhood improve, but it does protect this organizations place of primacy as a source of blessing to the neighborhood.