Question: I have a Pivot table in excel that is using a raw table as its data source. This pivot table is doing a bunch of grouping and summing of rows. 

I'd like to now use the result of this new pivot table as the data source for a new pivot table which will further modify this data. 

Is this possible with excel? I suppose you could call it 'nested pivot tables'

Answer: 
I guess your end goal is to show Distinct (unique) values inside your original Pivot table.

For example you could have data set with
OrderNumber, OrderDate, OrderItem, orderQty

First pivot table will show you OrderDate and sum of OrderQty **and you probably want to see Count of unique orders in the same Pivot**.
You woudln't be able to do so within standard pivot table 

If you want to do it, you would need Office 2016 (or perhaps pover Pivot might work). 
In office 2016 select your data > Insert > Pivot Table > **choose tick "Add this data to the Data Model"**

After that, you would be able to select grouping method as Distinct (Count)
As suggested you can change the pivot table content and paste as values.
But if you want to change the values dynamically the easiest way I found is
Go To `Insert->create pivot table`
Now in the dialog box in the input data field select the cells of your previous pivot table.