The ESFRI projects in ESCAPE will provide open access to their data, software and science tools to allow reproducibility of science results and the development of open science analyses across domains and infrastructures, necessary for opening the window to multi-messenger and multi-probe research. The aim of ESCAPE WP3-OSSR (Open-source Scientific Software and Service Repository) is to provide the tools necessary for the communities to share their science products in a harmonised way respecting the FAIR principles, promoting open science and maximising cross-fertilisation by software re-use and co-development. One of the key components to achieve this goal is the software repository. The present conceptual design report documents the work to build a demonstrator for the ESCAPE repository and provide an integrated development platform.