Unlike DOS games classes are far more structured in Dnd games, we can't decide what classes our companions/origin character will be at the start, but certain classes develop their specialisations at a later level, usually 3 or 2. We cannot make Shadowheart not worship Shar or make Wyll a different patron for his pact because they are part of their character backgrounds. Multiclassing is possible provided you meet the criteria and conditions, but it's tricky and we can only level up to level 10 so developing your party is critically important.
Interesting. I had suspected as much with the classes being so intertwined with the background stories/story plot of several, but not all, companions. Do you have a link to an interview or some such where Larian mentions this?