Realistic　network-like　systems　are　usually　composed　of　multiple　networks　with　interacting　relations　such　as　school-enterprise　research　and　development　(R&D)　collaboration　networks.　Here,　we　study　the　percolation　properties　of　a　special　class　of　R&D　collaboration　network,　namely　institute-enterprise　R&D　collaboration　networks　(IERDCNs).　We　introduce　two　actual　IERDCNs　to　show　their　structural　properties,　and　we　present　a　mathematical　framework　based　on　generating　functions　for　analyzing　an　interacting　network　with　any　connection　probability.　Then,　we　illustrate　the　percolation　threshold　and　structural　parameter　arithmetic　in　the　sub-critical　and　supercritical　regimes.　We　compare　the　predictions　of　our　mathematical　framework　and　arithmetic　to　data　for　two　real　R&D　collaboration　networks　and　a　number　of　simulations.　We　find　that　our　predictions　are　in　remarkable　agreement　with　the　data.　We　show　applications　of　the　framework　to　electronics　R&D　collaboration　networks.