To improve the statistics of hierarchical multiplicity, secondary components of wide nearby binaries with solar-type primaries were surveyed at the SOAR telescope for evaluating the frequency of subsystems. Images of 17 faint secondaries were obtained with the SOAR Adaptive Module that improved the seeing; one new 0.2'' binary was detected. For all targets, photometry in the g', i', z' bands is given. Another 46 secondaries were observed by speckle interferometry, resolving 7 close subsystems. Adding literature data, the binarity of 95 secondary components is evaluated. We found that the detection-corrected frequency of secondary subsystems with periods in the well-surveyed range from 10^3^ to 10^5^ days is 0.21+/-0.06--same as the normal frequency of such binaries among solar-type stars, 0.18. This indicates that wide binaries are unlikely to be produced by dynamical evolution of N-body systems, but are rather formed by fragmentation.