As cybercriminals scale up their operations to increase their profits or inflict greater harm, we argue that there is an equal need to respond to their threats by scaling up cybersecurity. To achieve this goal, we have to develop a co-productive approach towards data collection and sharing by overcoming the cybersecurity data sharing paradox. This is where we all agree on the definition of the problem and end goal (improving cybersecurity and getting rid of cybercrime), but we disagree about how to achieve it and fail to work together efficiently. At the core of this paradox is the observation that public interests differ from private interests. As a result, industry and law enforcement take different approaches to the cybersecurity problem as they seek to resolve incidents in their own interests, which manifests in different data sharing practices between both and also other interested parties, such as cybersecurity researchers. The big question we ask is can these interests be reconciled to develop an interdisciplinary approach towards co-operation and sharing data. In essence, all three will have to co-own the problem in order to co-produce a solution. We argue that a few operational models with good practices exist that provide guides to a possible solution, especially multiple third-party ownership organisations which consolidate, anonymise and analyse data. To take this forward, we suggest the practical solution of organising co-productive data collection on a sectoral basis, but acknowledge that common standards for data collection will also have to be developed and agreed upon. We propose an initial set of best practices for building collaborations and sharing data and argue that these best practices need to be developed and standardised in order to mitigate the paradox.