Dear Jérémie,
I understand that these groups are spurious, in the sense that they appear as (marginally) supported while a method to estimate group support should get zero support for them. A common procedure to circunvent this effect is calculating frequencies over the strict consensus of the optimal trees, instead of calculating a majority-rule consensus. In TNT, save the consensus as a tree X, then resampling > use groups from tree X.
That being said, it is true that these spurious groups have some support, just overturned in the entire dataset by the support of other competing groups (like a secondary signal). One may be interested in discussing how much evidence, or what characters, are in favor of some special suboptimal resolution - but the spurious groups generated by resampling may not be the right tool to find the interesting ones. People often explore alternative resolutions from historical interest, support from characters of special significance, or support from data partitions.
I have implemented some of the above ideas in a study (
https://doi.org/10.1206/821.1 page 13, Evaluation of alternative resolutions). There are also many studies cuantifying degree of support for alternative resolutions of a clade (e.g.,
https://doi.org/10.1016/j.asd.2018.05.002).
I hope this helps.
Best wishes,
Martin J. Ramirez
Curador y Jefe, División Aracnología / Curator & Head, Division of Arachnology
Museo Argentino de Ciencias Naturales - CONICET
Av. Angel Gallardo 470
C1405DJR Buenos Aires
Argentina