There are various tests one can administer to a tree. One of them is to permit one or more extra steps beyond the minimum to see where the weaknesses and strengths lay.
The following four illustrations show the Archosauria and their ancestors from fully resolved (Fig. 1) to what happens when 1, 2 and 3 extra steps are permitted (Figs 2-4).
Some large clades are retained while closest kin lose resolution, as expected. More characters specific to certain clades would help them keep resolution. Note that the major clades retained their distinction from other major clades.
Only more taxa can increase the possibilities for novel nestings by offering more possible nesting sites. More characters cannot provide more nesting opportunities. More characters can refine nestings within a limited range and/or they can strengthen established nestings by finding more synapomorphies (shared traits).
Any other insights would be gratefully appreciated.