MOTIVATION: The recent discovery of numerous non-coding RNAs (long non-coding RNAs, in particular) has transformed our perception about the roles of RNAs in living organisms. Our ability to understand them, however, is hampered by our inability to solve their secondary and tertiary structures in high resolution efficiently by existing experimental techniques. Computational prediction of RNA secondary structure, on the other hand, has received much-needed improvement, recently, through deep learning of a large approximate data, followed by transfer learning with gold-standard base-pairing structures from high-resolution 3-D structures. Here, we expand this single-sequence-based learning to the use of evolutionary profiles and mutational coupling. RESULTS: The new method allows large improvement not only in canonical base-pairs (RNA secondary structures) but more so in base-pairing associated with tertiary interactions such as pseudoknots, noncanonical and lone base-pairs. In particular, it is highly accurate for those RNAs of more than 1000 homologous sequences by achieving >0.8 F1-score (harmonic mean of sensitivity and precision) for 14/16 RNAs tested. The method can also significantly improve base-pairing prediction by incorporating artificial but functional homologous sequences generated from deep mutational scanning without any modification. The fully automatic method (publicly available as server and standalone software) should provide the scientific community a new powerful tool to capture not only the secondary structure but also tertiary base-pairing information for building three-dimensional models. It also highlights the future of accurately solving the base-pairing structure by using a large number of natural and/or artificial homologous sequences. AVAILABILITY: Standalone-version of SPOT-RNA2 is available at https://github.com/jaswindersingh2/SPOT-RNA2. Direct prediction can also be made at https://sparks-lab.org/server/spot-rna2/. The datasets used in this research can also be downloaded from the GITHUB and the webserver mentioned above.