Dark matter clusters on all scales, and it is therefore expected that even substructure should host its own substructure. Using the Extragalactic Distance Database, we searched for dwarf-galaxy satellites of dwarf galaxies, that is, satellite-of-satellite galaxies, corresponding to these substructures of substructure. From investigation of Hubble Space Telescope data for 117 dwarf galaxies, we report the discovery of a previously unknown dwarf galaxy around the ultra-diffuse M96 companion M96-DF6 at 10.2 Mpc in the Leo-I group. We confirm its dwarf-galaxy nature as a stellar overdensity. Modeling its structural parameters with a growth-curve analysis, we find that it is an ultrafaint dwarf galaxy with a luminosity of 1.5 x 10(5) L-circle dot, which is 135 times fainter than its host. Based on its close projection to M96-DF6, it is unlikely that their association occurs simply 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 (approximate to 10 000) than observed (approximate to 100), excluding the Large and Small Magellanic Cloud (LMC/SMC) 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-circle dot, the regime of the classical dwarf galaxies. However, simulated dwarf models at both a lower (< 10(6) M-circle dot) and higher (> 10(8) M-circle dot) stellar mass have comparable luminosity ratios. For the higher-stellar-mass systems, the LMC/SMC system is reproduced by simulations; for the lower stellar masses, no observed satellite-of-satellite system has been observed to date. More observations and simulations of satellite-of-satellite systems are needed to assess whether the luminosity ratio is at odds with ?CDM.