The extent to which predatory journals can harm scientific practice increases as the numbers of such journals expand, in so far as they undermine scientific integrity, quality, and credibility, especially if those journals leak into prestigious databases. Journal Citation Reports (JCRs), a reference for the assessment of researchers and for grant-making decisions, is used as a standard whitelist, in so far as the selectivity of a JCR-indexed journal adds a legitimacy of sorts to the articles that the journal publishes. The Multidisciplinary Digital Publishing Institute (MDPI) once included on Beall's list of potential, possible or probable predatory scholarly open-access publishers, had 53 journals ranked in the 2018 JCRs annual report. These journals are analysed, not only to contrast the formal criteria for the identification of predatory journals, but taking a step further, their background is also analysed with regard to self-citations and the source of those self-citations in 2018 and 2019. The results showed that the self-citation rates increased and was very much higher than those of the leading journals in the JCR category. Besides, an increasingly high rate of citations from other MDPI-journals was observed. The formal criteria together with the analysis of the citation patterns of the 53 journals under analysis all singled them out as predatory journals. Hence, specific recommendations are given to researchers, educational institutions and prestigious databases advising them to review their working relations with those sorts of journals.