Was actually thinking more of Liverpool - Leeds and Leeds - Sheffield with the added capability of break of journey at points in the Greater Manchester area.
South and West Yorkshire PTEs have common boundary stations at ...
SOUTH ELMSALL on Doncaster to Leeds line
MOORTHORPE on Sheffield to Leeds via Dearne line
DARTON on Barnsley to Wakefield Kirkgate line
DENBY DALE on Barnsley to Huddersfield line.
South Yorkshire One Day Travel Master ticket covers buses, tram and trains (to the above stations). West Yorkshire Day Rover, train only or bus and train (to above stations). See the respective PTE websites on advance purchase of 'scratch off' versions of the tickets. SY tickets can be purchased at PTE Travel Centres ( Sheffield interchange, Rotherham Interchange, Meadowhall Interchange, Doncaster Interchange) but I don't think you can buy them at stations. You cannot buy them on trains, trams or buses. There is also a SY Daytripper ticket that can be purchased from bus drivers and is valid on trains after 09.30 (m-F).
West Yorkshire Day Rovers can be bought at stations in WY, bus stations and at Post Offices (if there any still open!). Train Day Rovers can be bought from conductors on Northern trains.
Cross border journey trips can only be made on Northern services as these stop at boundary station (WY condition) and not sure about Leeds - Sheffield (&Nottingham) semi fast services. Only WY ticket valid on East Coast and only between Wakefield and Leeds and as far as Keighley / Horsforth.
On XC only valid Sheffield - Doncaster, or Wakefield - Leeds, but NOT from SY to WY or return!
Latest info on websites.
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Both South and West Yorkshire tickets are valid to the boundary stations of Darton, Denby Dale, Moorthorpe and South Elmsall so there's no need to buy a ticket to bridge the gap. Only works on the trains though AFAIK there's no similar arrangement on buses.
Cross border bus travel using both tickets is straight forward as all "border crossings" are at the location where the route passes from SY into WY or v.v.