I've submitted this separately to the proposed code market idea as the purpose is expressly to NOT share code - which is often hard to translate across departments due to platforms, copyright and security.
However government project documentation can be easily shared. It is generally created by, or totally owned by government and it is often platform independent.
For example, the requirements, design and technical specifications for a grant-management system, a blog, a wiki, a brainstorming site, are very similar across departments. So rather than having each department create their own documentation (sometimes missing important requirements) - why can't we share this documentation via a central site - then allow government departments to freely copy, amend and adapt this material for their specific needs - then resubmit their final version to be part of the common knowledge pool.
This would provide a structured way for government to build on learnings across the public sector, and encourage more standardised approaches to documentation and to factors like accessibility and usability.
As a secondary consideration, departments who want to build an X (online), but are not fully funded to do so, could put up a wishlist of their projects, which could be matched against other agencies who want similar or identical online functionality.
Where there are sufficient matches, the agencies could get together to jointly fund the project - leveraging better use of government funds and providing a superior outcome for all the agencies involved. Naturally the final implementation could be individually customised by agencies for their technical platform and specific needs (outside the shared needs) - but they could afford to pay for this as they would not need to afford to build the entire thing from scratch.
Of course there are various government procurement and other legal, technical, governance and other matters that would need to be considered - however this approach could result in significant savings across the public sector.
It does require that government operate more as a single organisation, than as a set of extremely different organisations - but not that much.
This concept could be easily extended beyond the government sector into the commercial world - just in case the government wanted to spin-off a start-up.