Question 

Can you have different completeness rules for different products? We are in the start of our PIM implementation and want to learn more about what is possible with Completeness. 

Answer

With the out-of-the-box completeness rules it is currently not possible to have different completeness criteria for specific products, say based on Fieldset. However, the intended way of using Completeness is to cover the general completeness rules in your enriching process to understand how complete your entity is. You can then group the Completeness criteria into different Completeness Groups and a typical implementation approach is to use this grouping from a channel perspective, for example if the product is "Print ready" or "Web ready" etc.

These Completeness Groups could then be utilized in the Channel Insight overview in Plan & Release, where a user then can see "how ready" a channel is for each entity type.

There is also the possibility to implement Custom Completeness Criteria’s that allows specialized rules.

There are a lot of great articles on Completeness, start with the below and continue from there. 

Related articles 

Completeness levels

Completeness

Custom completeness criteria