Natively monomeric RNase A can oligomerize upon lyophilization from 40% acetic acid solutions or when it is heated at high concentrations in various solvents. In this way, it produces many dimeric or oligomeric conformers through the three-dimensional domain swapping (3D-DS) mechanism involving both RNase A N- or/and C-termini. Here, we found many of these oligomers evolving toward not negligible amounts of large derivatives after being stored for up to 15 months at 4 °C in phosphate buffer. We call these species super-aggregates (SAs). Notably, SAs do not originate from native RNase A monomer or from oligomers characterized by the exclusive presence of the C-terminus swapping of the enzyme subunits as well. Instead, the swapping of at least two subunits’ N-termini is mandatory to produce them. Through immunoblotting, SAs are confirmed to derive from RNase A even if they retain only low ribonucleolytic activity. Then, their interaction registered with Thioflavin-T (ThT), in addition to TEM analyses, indicate SAs are large and circular but not “amyloid-like” derivatives. This confirms that RNase A acts as an “auto-chaperone”, although it displays many amyloid-prone short segments, including the 16–22 loop included in its N-terminus. Therefore, we hypothesize the opening of RNase A N-terminus, and hence its oligomerization through 3D-DS, may represent a preliminary step favoring massive RNase A aggregation. Interestingly, this process is slow and requires low temperatures to limit the concomitant oligomers’ dissociation to the native monomer. These data and the hypothesis proposed are discussed in the light of protein aggregation in general, and of possible future applications to contrast amyloidosis.