There are fewer companions available to the Avatar in Serpent Isle as compared to the Black Gate. Typically, the Avatar can have at most four companions, but there is a time this limit can be exceeded, however the game may crash or experience general problems.
One way to obtain a fifth character is to kill an existing party member, recruit the new member, then resurrect the fallen member. This can also be done by casting Serpent Bond, then recruiting the new teammate and letting the spell wear off. If the party consists of more than six characters, the game will crash whenever the Combat Status Display is brought up.
The main companions are absolutely necessary for certain sequences in the game, but the Avatar could be rid of them at other times. Most alternative companions fair poorly in comparison, though.
Dupre: The strongest of the starting companions, he's the best starting melee character.
Iolo: Starts with very low Strength, but good Dexterity. Somehow he became weaker than his starting stats in Ultima VII: The Black Gate. Due to his low health, he's best at the rear with a ranged weapon.
Shamino: Splits the difference between Dupre and Iolo; he has somewhat better Strength than Iolo as well as slightly worse Dexterity.
Automaton: This metal constructs can be revived using the Create Automata spell. Their stats are fixed and they cannot be trained. Most status and environmental conditions do not affect them. They are only useful when any of the main companions are not available.
Boydon: Starts with maximum Strength. Both his Dexterity and Combat can be maxed out if he reaches Level 8. Caution should be exercised in battle and during certain events as Boydon cannot be revived if he dies.
Petra: Can join the party as part of the quest to the Temple of Discipline, however she isn't necessarily required. Therefore, she can be "tricked" into permanently joining the party by simply completing the quest without her, then asking her to join. Her stats are a little better than the average Automaton, but she can be trained.
Wilfred: Located in Sleeping Bull, he can only join late in the game. He throws tantrums if he is badly wounded or is asked to leave the party. Wilfred will never re-join the party in either case, so he is basically a one-shot companion. He cannot even be revived with the Hourglass of Fate.
Gwenno: Located in Monk Isle, but she join only after Dupre died.
Selina: Temporarily joins as part of quest, she'll leave the group if the Avatar strays too far from the objective.
Stefano: Joins during a quest in Mountain of Freedom, he's stats are abysmal. His lowest stat is Combat with a rating of two (2).
Mortegro: At some point, he can join the party, but he is even weaker than Stefano. He can be added permanently by either abusing Serpent's Bond or the Hourglass of Fate. However, once he joins, he can never leave (unless he dies).
Sethys: Temporarily joins as part of quest, he'll die once he is outside. He can be added permanently by either abusing Serpent's Bond or the Hourglass of Fate.