This article explores the potential approaches to optimising the way the institutions of mutual common use by the BRICS countries are constructed. The topic is time-relevant, for it reveals the need to work out a new institutional basis to understand the workings of the BRICS institutions as a result of recent transformations, such as Brexit, in the phenomenon of international and regional economic integration. The article is founded on the hypothesis that the import of institutions by the BRICS may be a more effective approach to the member countries’ convergence than the conventional approach. The originality of the theme lies in the fact that the modern economic literature has not studied to the full extent the impact of this exogenous factor on financial integration. There is also a need for the further development of the least-studied areas of regional monetary integration, namely the lack of the ability of current world institutions to manage the common monetary policies and debt of the member countries. The author proposes principles for creating and operating a virtual contractual republic of the BRICS contrary to the exploitation-state model of the EU. The article rediscovers the institutionalist idea about democratic decisions by a group of subjects such as the member countries of a particular integration agreement. The author maintains that the new institutions of the BRICS may cause dramatic changes in the world monetary system, international liquidity and international reserves. The general conclusions of the article encompass the significance of creating integration institutions on the basis of the experience of the BRICS as a way to more economic and financial stability in the world. The results contribute to the search for opportunities of optimal operation of the BRICS regional debt market. In his closing remarks, the author outlines the prospects of settling the debt problems in the BRICS based on the virtual debt market.