Yes. The total amount of third party funding would be subtracted from the original incremental cost applied to the original calculated incentive amount. This updated incremental cost would then be applied and a new incentive amount would be calculated.
Custom Program example
For example, if you have a project with a $77,000 incremental cost, that will produce 2,829 tC02e of lifetime GHG savings, your maximum eligible incentive will be $38,500 (50% of incremental cost). If you have received $10,000 from a third-party towards that same project, the Custom Program incentive would be recalculated to $33,500 ($77,000-10,000= $67,000 incremental cost).
Custom-Lite example
For example, if you have a project with a $25,000 incremental cost that will produce 1,000 tCO2e of lifetime GHG savings, your maximum eligible Custom-Lite Capital Incentive will be $12,500 (50% of incremental cost). If you have received $5,000 from a third-party towards that same project, the Custom-Lite Capital Incentive would be recalculated to $10,000 ($25,000-5,000= $20,000 incremental cost).