I know that Shaw don't support what I'm asking, but hopefully someone may be able to help.

Few months ago Shaw tech visited and enable Gateway and 4 portals, have Moca filter (4-way splitter) at the shaw box entering the home. Have Internet 300, and XB6 router on the middle (main) floor of our 3 floor townhouse (4 coax wall sockets - all enabled). I'm looking to connect up some Actiontec ECB6200 adapters in order to get better internet speed into the basement / office instead of currently using another router as a repeater.

Have no ethernet wiring in the house. 

Currently have 2 x 2-way splitters, if I replace the 2-way splitters with 3-way splitters (any recommendations on brands etc) and connect the ECB6200's to the living room where the XB6 router and in the basement / office would that work?

Below is what I think the future proposed solution may look like if its possible? 

Thanks in advance.