The dislike chart would seem to suggest the following combinations are possible without any dislikes and that it's possible to mix and match the tops with the bottoms without any dislikes.
Top 1:
- Alayen
- Firentis
- Baheshtur
Top 2:
- Nizar
- Katrin
- Marnid
Bottom 1:
- Borcha
- Artimenner
- Matheld
- Lezalit
- Rolf
Bottom 2:
- Klethi
- Jeremus
- Ymira
- Bunduk
- Deshavi
It is possible to keep two people who dislike each other and not have them leave. Balance the dislike out with someone they like and keep morale high.
Some forum posts seem to suggest that it's possible to even keep all 16 if one manages morale. Keep the morale around 80-99, don't lose and keep them stuffed with food. Do not rob villages. Raid caravans only when Marnid isn't around.
There is an idea of having two 8 members companions. One traveling for a battle, when the other is healing in castle.
It is possible to have a 10 heroes party with everyone getting 1 "like" and 1 "dislike" or none of each, so it should be easier to maintain them all in the party:
Alayen, Ymira, Nizar, Matheld, Artimenner, Borcha, Rolf, Baheshtur, Bunduk, Katrin.
For a comparison of the different companions' skills and abilities see Here
Further reading: