We reinvestigated the neutron multiplicity yields of Ba-Mo, Ce-Zr, Te-Pd, and Nd-Sr from the spontaneous fission of $^{252}$Cf; by (i) using both $gamma$-$gamma$-$gamma$-$gamma$ and $gamma$-$gamma$-$gamma$ coincidence data, (ii) using up to date level scheme structures, and (iii) cross-checking analogous energy transitions in multiple isotopes, we have achieved higher precision than previous analyses. Particular attention was given to the Ba-Mo pairs where our results clearly confirm that the Ba-Mo yield data have a second hot fission mode where 8, 9, 10, and now 11 neutron evaporation channels are observed. These are the first observations of the 11 neutron channel. These 8-11 neutron channels are observed for the first time in the Ce-Zr pairs, but are not observed in other fission pairs. The measured intensities of the second mode in Ba-Mo and Ce-Zr pairs are $sim$1.5(4)$%$ and $sim$1.0(3)$%$, respectively. These high neutron number evaporation modes can be an indication of hyperdeformation and/or octupole deformation in $^{143-145}$Ba and in $^{146,148}$Ce at scission to give rise to such high neutron multiplicities.
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