I hired all companions to my party and wrote down who dislikes who. These are the results:

Adalwin: Bruno, Onuist.
Aelius: Bruno, Chlodulf.
Agasicles: Narses, Chlodulf.
Aldric: Tahmasp, Avila.
Alisher: Costin, Avila.
Avila: Alisher, Aldric.
Bagadata: Narses, Eithne.
Bruno: Adalwin, Caratacos.
Chlodulf: Agasigles, Aelius.
Ciniod: Agasicles, Aelius.
Clovis: Eadfrith, Matui.
Connor: Ultan, Clovis.
Costin: Alisher, Titus.
Eadfrith: Ultan, Matui.
Eadwine: Eadfrith, Mihael.
Eithne: Bagadata, Caratacos.
Inka: Ciniod, Onuist.
Matui: Connor, Clovis.
Mihael: Eadfrith, Eadwine.
Narses: Agasicles, Bagadata.
Onuist: Bruno, Narses.
Tahmasp: Aldric, Titus.
Titus: Costin, Tahmasp.
Ultan: Eadfrith, Onuist.

I should have written down who likes who, their personality and if they are noble/commoner; missed opportunity there.

Inka is not disliked by anyone (and is liked by some four or five); Eadfrith is disliked by four; Agasicles, Aldric, Bruno, Narses and Onuist are disliked by three, each; Ceawlin, Ciniod, Connor, Eadwine and Mihael are disliked by only one, each.

With the above information I managed to select a group of twelf where nobody is disliked by any of the others: Aldric, Alisher, Bruno, Ceawlin, Chlodulf, Eithne, Inka, Narses, Titus, Ultan, (Clovis or Matui), (Eadwine or Mihael). I have not exausted all possibilities in this search, so maybe there is some larger group possible.