Multidimensional data have become ubiquitous and are frequently encountered in situations where the information is aggregated over multiple data atoms. The aggregation can be over time or other features, such as geographical location. We often have access to multiple aggregated views of the same data, each aggregated in one or more dimensions, especially when data are collected or measured by different agencies. For instance, item sales can be aggregated temporally, and over groups of stores based on their location or affiliation. However, data mining and machine learning models benefit from detailed data for personalized analysis and prediction. Thus, data disaggregation algorithms are becoming increasingly important in various domains. The goal of this paper is to reconstruct finer-scale data from multiple coarse views, aggregated over different (subsets of) dimensions. The proposed method, called PREMA, leverages low-rank tensor factorization tools to fuse the multiple views and provide recovery guarantees under certain conditions. PREMA can tackle challenging scenarios, such as missing or partially observed data, double aggregation, and even blind disaggregation (without knowledge of the aggregation patterns) using a variant of PREMA called B-PREMA. To showcase the effectiveness of PREMA, the paper includes extensive experiments using real data from different domains: retail sales, crime counts, and weather observations.