User blog comment:Undeadlift/Very Fast Growing Hierarchy/@comment-2A02:8108:4A40:A764:F8DF:6165:64B7:A588-20171025185148/@comment-28606698-20171025190128

It is possible of course, but difference with standard fast-growing hierarchy will be only up to $$f_{\omega^2}(n)$$,