Gas turbine engine system and operation method for exhaust gas use in gas turbine engines

A method of operation of a gas turbine engine system and a gas turbine engine system (50,120,130,200) are provided that include a first gas turbine engine (52). The first gas turbine engine (52) has a first compressor (80) configured to intake air and to produce a first compressed air (14) and a first combustor (88) configured to combust a first mixture to produce a first combustion gas. The first mixture has a first fuel, at least a first portion of the first compressed air (14), and a second combustion gas (24) from a second gas turbine engine (10). The first gas turbine engine (52) also includes a first turbine (92) configured to extract work from the first combustion gas.