How does the influence of interest groups and political parties differ from a multi-party system to a two-party system?
In a multi-party system, political parties typically have more influence and interest groups have less. This is particularly true in a system with proportional representation.
There are two reasons for this.
First, parties in such systems tend to have control over their candidate lists. That is, they tend to be able to decide who gets to run for office and who does not. That gives them much more power than interest groups because a person torn between doing what the interest group wants and what the party wants knows that they have to go with the party or risk losing their seat. This typically cannot happen in a two-party system with primaries like the US has.
Second and more importantly, multi-party systems have more focused political parties. When you only have two parties, each party has to try to be almost all things to all people. This leaves a lot of room for interest groups to have influence because the parties are not focused on single issues. The parties are trying to please everyone so interest groups are needed to push on single issues. In a multi-party system there are so many more parties that are based on narrower interests. In such a system, interest groups are less important because each party is more focused and more like an interest group itself.