Combined analysis of multiple, large datasets is a common objective in the health- and biosciences. Existing methods tend to require researchers to physically bring data together in one place or follow an analysis plan and share results. Developed over the last 10 years, the DataSHIELD platform is a collection of R packages that reduce the challenges of these methods. These include ethico-legal constraints which limit researchers' ability to physically bring data together and the analytical inflexibility associated with conventional approaches to sharing results. The key feature of DataSHIELD is that data from research studies stay on a server at each of the institutions that are responsible for the data. Each institution has control over who can access their data. The platform allows an analyst to pass commands to each server and the analyst receives results that do not disclose the individual-level data of any study participants. DataSHIELD uses Opal which is a data integration system used by epidemiological studies and developed by the OBiBa open source project in the domain of bioinformatics. However, until now the analysis of big data with DataSHIELD has been limited by the storage formats available in Opal and the analysis capabilities available in the DataSHIELD R packages. We present a new architecture ("resources") for DataSHIELD and Opal to allow large, complex datasets to be used at their original location, in their original format and with external computing facilities. We provide some real big data analysis examples in genomics and geospatial projects. For genomic data analyses, we also illustrate how to extend the resources concept to address specific big data infrastructures such as GA4GH or EGA, and make use of shell commands. Our new infrastructure will help researchers to perform data analyses in a privacy-protected way from existing data sharing initiatives or projects. To help researchers use this framework, we describe selected packages and present an online book (https://isglobal-brge.github.io/resource_bookdown).