Illustrator provides two ways to access Next Object commands:
1. From Select menu
2. From the context menu, Select submenu

And while the context menu provides four commands, the Select menu gives only two. First Object Above / Last Object Below — for no apparent reason — are missing, and we can’t assign hotkeys to these because of it.

Please add them there.

Also consider this request, to be able to select ALL objects above or below the current selection: https://illustrator.uservoice.com/forums/333657-illustrator-desktop-feature-requests/suggestions/34306246-select-objects-above-below-current-layer-objec

Note that this one is basically about 'select those who intersect', while we are also interested in 'select those which are above below in stack'.

Finally, here is a bug report about Select Next Object commands in context menu (and only these, not their main Select menu analogs) not working at all: https://illustrator.uservoice.com/forums/601447-illustrator-desktop-bugs/suggestions/46742011-select-next-object-commands-in-context-menu-are-br