MAXDOP recommendation
Change MAXDOP from 0 to 6? Are we likely to gain anything from
  changing this setting?


The short answer is: it depends on your workload and the cpu usage of your queries.


  Example 1:


What is your CPU usage, are you seeing spikes on certain queries, are these queries bottlenecking other queries?

If the answer is yes

consider changing your maxdop to 2 or 4. Also, check your cost threshold for parallellism, if this is at the default of 5, consider setting this higher, but as always, monitoring your workload before and after is key.


  Example 2:


This one is a bit tricky, since one instance could hog all the resources on your machine. 

An important factor in this example is determining which instances are the most critical to always run their queries without possible bottlenecking of the other  five instances. 

Monitor workload before and after, but leaving it at 0 for all instances and having big queries running at 2 or more instances will cause bottlenecks.

I would consider again setting it to 2 for less important instances and 4 for more important instances to start with, and change this again based on the results. (Here also consider the cost threshold for parallellism setting).