Critical evolution PDEs may have solutions forming a singularity in finite time with anomalous self-similarity. There are now numerous examples where a soliton (here a stationary state or a traveling wave) collapses at a point due to its interactions with the remainder of the solution. Much less is known about singularities formed by several solitons collapsing simultaneously at a single point, especially in the non-radial case. The first example was constructed for the nonlinear Schrodinger equation by Martel-Raphael [Ann. Sci. ENS 2018]. I will present examples of such solutions for the parabolic-elliptic Keller-Segel system in two dimensions [joint work with Ghoul-Masmoudi-Nguyen 2024] and for the cubic wave equation in four dimensions [ongoing joint work with Li to appear]. The associated patterns are caused by different effects for each equation: the solitons' own dynamics, their interactions, and their interactions with the remainder of the solution which is affected by the presence of the multiple nearby potentials from the solitons. I will present ideas for the construction of an approximate solution, and its stability analysis based on the control of its modulating parameters and of suitable norms for the remainder, adapted to the multiscale feature of the problem.