Dark matter clusters on all scales, therefore it is expected that even substructure should host its own substructure. Using the Extragalactic Distance Database, we searched for dwarf galaxy satellites of dwarf galaxies, i.e. satellite-of-satellite galaxies, corresponding to these substructures-of-substructure. Going through HST data of 117 dwarf galaxies, we report the discovery of a dwarf galaxy around the ultra-diffuse M96 companion M96-DF6 at 10 Mpc. Modelling its structural parameters, we find that it is an ultra-faint dwarf galaxy which is 135 times fainter than its host. Based on its close projection to M96-DF6 it is unlikely that their association occurs by chance. We compare the luminosity ratio of this and three other known satellite-of-satellite systems with results from two different cosmological sets of CDM simulations. For the observed stellar mass range of the central dwarf galaxies, the simulated dwarfs have a higher luminosity ratio between the central dwarf and its first satellite ($\approx$10'000) than observed ($\approx$100), excluding the LMC system. No simulated dwarf analog at these observed stellar masses has the observed luminosity ratio. This cannot be due to missing resolution, because it is the brightest subhalos that are missing. This may indicate that there is a satellite-of-satellite (SoS) problem for CDM in the stellar mass range between 10$^6$ and 10$^8$ M$_\odot$ - the regime of the classical dwarf galaxies. However, simulated dwarf models at both a lower ($10^8$ M$_\odot$) stellar mass have comparable luminosity ratios. For the higher stellar mass systems, the LMC system is reproduced by simulations, for the lower stellar masses, no observed SoS system has been observed to date. More observations and simulations of SoS systems are needed to assess whether the luminosity ratio is at odds with CDM.

Comment: 8 pages, 7 figures, 3 tables. Accepted for publication in Astronomy & Astrophysics. Abstract shortened due to arxiv abstract length requirements