On the UK rail network, multiple working is where two or more traction units (locomotives, diesel multiple units or electric multiple units) are coupled together in such a way that they are all under the control of one driver (multiple-unit train control).
If the front locomotive of a pair in multiple has failed the driver can still control the rear locomotive for as long as air and electricity supplies are available on the failed locomotive.
Many main-line diesel-electric and hydraulic locomotives are capable of running in multiples of up to three under the control of one driver
— British Railways Diesel Traction Manual for Enginemen, [1]
In tandem is when more than one diesel or electric locomotive are hauling a single train and under the control of a driver on each locomotive.