This paper extends an earlier work "The social construction of consciousness - A socio-cultural perspective on language based consciousness" which focused on a major aspect of consciousness: namely, reflectivity. It was argued that the problem of consciousness can be fruitfully approached by beginning with human group and collective phenomena: community, language, language-based communications, institutional and cultural arrangements, collective representations, and self-referentiality. Collective reflectivity emerges as a function of a group or organization producing and making use of language-based collective representations of the self ("we", our group, community, organization, nation). A collective monitors its judgments, activities, achievements and failures and reflects on itself, its properties, its previous judgments and actions, and its future plans as a defined and on-going collective being. The reflectivity is encoded in language and developed in conversations and critical reflections about collective selves. It was also argued in the earlier work that individual consciousness is a natural outcome of the development of collective naming, classifying and discussing particular objects - where such objects may be group members or participants in collective activities. Through collective participation and experience of reflective communications, individuals acquire to a greater or lesser extent the a capability of self-reflection and self-dialogue. In this paper, the concept of collective and individual reflectivity - as a major aspect of consciousness - is extended through the development of the notion of meta-reflectivity, namely reflection on the properties, forms, processes, and outcomes of reflectivity. For instance, an agent considers and assesses the particular way she/he reflects, the frame, rules and standards of judgments, and programs or strategies for solving problems or dealing with crises through reflectivity. Meta-reflectivity entails phases of awareness about or attention to particular reflective practices, criticism or questioning of these, and processes for reconstructing them or generating new reflective forms and processes. Meta-reflectivity may result in the realization or establishment of a new standpoint for reflectivity, a standpoint entailing new concepts, norms, and strategies - which often entails also a transformation of self-conception. Two distinct forms of meta-reflectivity are discussed. Several biases and distortions in meta-reflective processes are identified and their implications analyzed. In particular, socially constructed and sanctioned mechanisms of cognitive stabilization (and resolution of dissonance and contradiction) may block or misdirect fruitful meta-reflectivity and the reconstruction of self under conditions of performance failures or crises.