Motivated by the novel asymptotically global AdS$_4$ solutions with deforming horizon in [JHEP {bf 1802}, 060 (2018)], we analyze the boundary metric with odd multipolar differential rotation and numerically construct a family of deforming solutions with tripolar differential rotation boundary, including two classes of solutions: solitons and black holes. We find that the maximal values of the rotation parameter $varepsilon$, below which the stable large black hole solutions could exist, are not a constant for $T> T_{schw}=sqrt{3}/2pisimeq0.2757$. When temperature is much higher than $ T_{schw}$, even though the norm of Killing vector $partial_{t}$ keeps timelike for some regions of $varepsilon<2$, solitons and black holes with tripolar differential rotation could be unstable and develop hair due to superradiance. As the temperature $T$ drops toward $T_{schw}$, we find that though there exists the spacelike Killing vector $partial_{t}$ for some regions of $varepsilon>2$, solitons and black holes still exist and do not develop hair due to superradiance. Moreover, for $Tleqslant T_{schw}$, the curves of entropy firstly combine into one curve and then separate into two curves again, in the case of each curve there are two solutions at a fixed value of $varepsilon$. In addition, we study the deformations of horizon for black holes by using an isometric embedding in the hyperbolic three-dimensional space. Furthermore, we also study the quasinormal modes of the solitons and black holes, which have analogous behaviours to that of dipolar rotation and quadrupolar rotation.
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