In this two examples, what could be the Pros and Cons? Are there any?
- Barbarian + Wizard + Monk + Monk
- Barbarian + Barbarian + Barbarian + Barbarian
As stated in the question about class roles, here, each class is designed to function as an independent unit.
This means that you are not penalized for having more than one of the same class. What you might gain, however, is highly variable, dependent on what classes you're stacking. Multiple monks, for instance, can give you more than one mantra, or... depending on their build... they might not use a mantra at all.
There is one consideration though: you don't want the duplicated classes to be using the same abilities (very likely at lower levels). Duplicate copies of the same buff will not stack with each other, but will instead reset the duration of the effect.
The best answer one can hope to offer is that you won't be hindered by having more than one of the same class, but there's no way to answer the other question (what characters synergize well together) in the most general case.