Worksheet Actions can do exactly what you want.
On your Tableau Worksheet, go to the top menu bar. Click Worksheet, and then click Actions...
And then when a little Actions pop-up comes up, select Add Action and select Filter.
A new window will popup:
Choose the "Source" sheet (the sheet that you have to click) and a "Target" sheet (the sheet that you will be redirected to, with a filter on it). Click Select so that when you select a region/store/product, it will auto-link and filter you to the next worksheet.
There you go!
You can also put them all on the same dashboard using Dashboard Actions (Dashboard > Actions... uses the exact same premise). It's very useful for dashboard drill-downs. There are also ways to make dashboard action filters sync with your dashboard quickfilters.
in your example
For example, sheet 1 shows sales by the following regions,
Northeast, Northwest, Southeast and Southwest. You select Northeast. Sheet #2 updates with Stores A, B, C and D
from that region. You select Store C and
Sheet 3 shows sales for Products A, B and E (C&D were not sold in Store C).
if we select the store c then it will filter c store sales products only in sheet 3.
First you can create filter action with sheet 1 and target the sheet 2.
2nd action create sheet 2 and target to sheet 3.
This is what u expected here.