2 specific secondary drop down lists can be chosen after chosen specific option in primary

If you create named lists you can reference them using the INDIRECT function, which it seems like you already know.

What I would recommend for sub list 2 is to include an IF statement or VLOOKUP, depending on how many options you need to choose.

Example:

Create two lists, one called BOX2A, which includes LOWER PART I and LOWER PART 2 and one called BOX2B, which includes LOWER PART P and LOWER PART Q.

In the data validation for your second drop-down use formula that references those list names based on what is in the main menu.

=INDIRECT(IF(A1="Item A","BOX2A",IF(A1="Item B","BOX2B","")))

Or you can create a table of list names that should be associated with each specific Item in the main menu, which would be more efficient if you have several items in the main menu.

=INDIRECT(VLOOKUP(A1,G1:H5,2,FALSE))

G1:H5 being where your table is located, 2 being the column within the table where the names for the appropriate lists for the 2nd dependent box are found.

Here's a video that covers using the INDIRECT function for the first part of what you'll need to do http://www.youtube.com/watch?v=0Ey8-ILjjYs