Collaborative Pareto Set Learning (CoPSL) has emerged as an effective approach for learning Pareto sets across multiple multi-objective optimization problems (MOPs) through shared and task-specific neural network layers. However, its performance depends critically on the sampling distribution of preference vectors, leading to suboptimal efficacy when handling MOPs with heterogeneous Pareto front geometries. To address this limitation, Pareto front shape-agnostic Pareto Set Learning (GPSL) eliminates preference dependency by reformulating the learning process as a distribution transformation problem. Building on these advances, this paper proposes a new multitasking multi-objective optimization framework: Collaborative GPSL (CoGPSL), which combines the collaborative learning structure with the distribution transformation mechanism. CoGPSL transforms arbitrary input distributions into task-specific Pareto set distributions. By maximizing the similarity between generated and true Pareto-optimal solutions, CoGPSL eliminates reliance on preference vectors sampling and ensures effective learning across multiple MOPs with heterogeneous front geometries in a single run. Experimental results show that the proposed CoGPSL can simultaneously handle MOPs with highly different shapes of the Pareto front and demonstrate a faster convergence rate compared with recent PSL algorithms and the CoPSL framework.