Is it possible (even if there is no reason to even want to do this) to expand the hyperreal number line at each infinitesimal to insert a "second layer of infinitesimals"?
Let $\epsilon$ be an infinitesimal hyperreal in the halo of $0$. Can we invent another level of infinitesimals that indicate a second-order-infinitesimal distance from infinitesimals so that relative to these second level infinitesimals, the hyperreal infinitesimals seem like real numbers?
E.g. like let $\delta=(\epsilon+1,\epsilon+\frac12,\epsilon+\frac13,\ldots)$ represent an infinitesimal in the "2nd-level-halo" of $\epsilon$.