You create a fundraising campaign specifically for that partnership. The main challenge would be to attract larger donors who feel tied to the common goal and ensure that the raised resources are sufficient to continue the work. And advantage could be the fact that neither party commits its resources or holds more power in the relationship.
Hosting a hackathon for the particular challenge that the partnership is trying to achieve. Through this approach you can gain visibility for the project, identify new potential partners and also secure funding from the public and donors.