Joint GN/GC Network in West Yorkshire?

[1165Valour]

I had considered posting this in my previous thread on the MS&LR/GCR gaining the Huddersfield line, but I decided it would be best to give it its own thread.

 

This scenario assumes that the Huddersfield & Manchester Railway remained in the MS&L camp, rather than eventually being absorbed by the LNWR. The MS&L now has a line to Leeds, and by the late 1850s the GN is also beginning to expand into the West Riding.

 

Assuming the GN and MS&L still eventually become allies, what would be the likelihood of the GN's West Yorkshire network being owned and operated jointly? In 1861, the LNW's plans to extend the Birstall branch to Bradford were defeated in favor of the GN proposal - could a joint GN/MS&L line via Birstall take its place?