The current stage of the BRICS countries’ cooperation opened a new page of interaction between the parties thereto, which encompasses various spheres and vectors of geographic, political, economic, social, and other sides of life of the above grouping with eventually aimed at more integrational targets and communitarian trends in the interstate links. Certain new formats of BRICS relationships in economics, science, technology, and innovations (‘BRICS+’, ‘BRICS-outreach”) that have recently emerged reflect the future path of the alliance and even to some extent the world development. Realization of modern tracks of cooperation requires the deployment of platforms for dialogue as well as for multilaterality, accompanied by creation and/or adjustment of legal mechanisms of interaction, especially in the fields of newest technologies and innovations, inevitably obtaining nowadays the extraordinary significance. BRICS serves nowadays to act as an evident center of influence within the relevant regions (Russia—through the Eurasian Economic Union (EAEU) and the Shanghai Cooperation Organization (SCO) in Eurasian subregion; China—in the South-East Asia as the leader of the Association of South East Asian Nations (ASEAN); India—in the South Asian Association for Regional Cooperation (SAARC) and ‘Bay of Bengal Initiative for Multi-Sectoral Technical and Economic Cooperation (BIMSTEC); Brazil—in Latin America and Caribbean region through the Southern Common Market (MERCOSUR—span.: Mercado Común del Sur, port.: Mercado Comum do Sul) alongwith the Community of Latin American and Caribbean States (CELAC—span.: Comunidad de Estados Latinoamericanos y Caribeños); the Republic of South Africa—within the African Union and the South African Development Community (SADC), etc.). The said circumstances suppose impressive extension of the alliance and respective availability of various combinations of mutual influence between basic and special principles within the regulatory system. Thus, the chapter discloses the impact of basic principles of international law along with the specific peremptory norms of general international law (jus cogens) upon the part of legal ground which is formed by the sectoral (special) guiding—or saying in other words—prevailing—rules of law jointly agreed by all members of the alliance.