  Using the renormalization group techniques it was previously shown that the
perturbative effective potential in the $\mathcal{O}(N)$ symmetric $\phi^4$
theory, massless scalar electrodynamics as well as in the conformal limit of
the standard model can be uniquely determined in terms of the known MS scheme
renormalization group functions. Furthermore, re-summation of the leading order
corrections plus portions of these higher order contributions to the effective
potential in the $\mathcal{O}(N)$ symmetric $\phi^4$ theory shows a peculiar
shift in the usual "Landau singularity" apparent in the individual leading
order corrections. In this work, we have further investigated this shift by
extending the result for theories having multiple couplings. We have shown that
the singularity structure of the effective potential as seen by summing up
portions of the $V_{N^{P+n}LL}$ for any finite $P$ is altered as expected when
these perturbative contributions are summed to all orders but more
significantly we found that this shift in the singularity is completely
determined by the one and two loop beta functions only. We argue that this is a
general result which applies to the conformally invariant standard model.
