How would I fit both a dishwasher and a washing machine with this plumbing?
Assuming you can physically fit a dishwasher and a washing machine between your cabinets, you would need to replace two parts.


Replace the trap under the sink with one that has connections for two appliances.
Replace the blue shut off valve with one that also has two connections. 


Here are a couple of parts that should work.




This is all feasible by a DIY'er but might require some extra fittings or cuts to the shelf to make the new trap fit. You might also be able to find a similar valve but push-fit and easier to install.