Collaboration is usually a positive, and the partners should be carefully chosen. Schedule a meeting of the team. Come to agreement on the key elements of the project. If private funding is the choice, do the necessary research to determine your best chances of being funded. Also consider the odds.
Grant writing takes time.
Don't spend it on something that has an unlikely reward. Don't forget that grants carry rewards and burdens. The most obvious plus is the opportunity to fund an exciting project for your school. The side benefits of team building and recognition are also worth mentioning. The downside is that a grant project will likely impact other school staff and this should be carefully considered when applying.