@wooch. You don't state what model year your car is, so 'it depends', but in simple terms - no, you can't just fit a centre speaker to a 380W audio system to gain centre channel sound. Jaguar fitted a range of amplifier, headunit, speaker combinations over the lifespan of the F-Type. Regardless of model year, the 380W amplifier does not have the ability to output a centre channel signal and although you will find a centre speaker fitted to MY19+ vehicles, this is not driven by the headunit/amplifier, but instead is used for the incoming voice signal by the Telematics Control Unit, during communication with the InControl centre in case of accident or SOS call. Cars prior to this, used the rear mids for communication.
For early model cars (prior to 2016), where the amplifier is fitted on the rear bulkhead inbetween the seats, it is possible to retrofit the (old pattern) 770W amplifier and a centre speaker. You then have to configure the CCF file with SSD to enable the surround sound functionality.
If you have a 5.0 litre F-Type with the characters LCK, MCK, NCK, PCK and RCK in the last eight characters of the VIN, it is possible to upgrade to surround sound without any hardware changes. This was due to Jaguar fitting higher spec hardware during a period of DSP chip shortage, to keep the order books going. See LR-Retrofits for details -->
https://lr-retrofits.co.uk/x152-f-type bottom of page.
Finally, LR-Retrofits also provide a 380W to 770W hardware/software upgrade for later models, but this will be dependant on your current individual headunit/amplifier communication technology (change from optical to ethernet). Once again, see LR-Retrofits for details.
After all that, based on what I have researched, most owners with the 770W system use the system in one of the stereo modes, not surround, as they feel the centre channel is too powerful and drowns out the variation between left and right channels, detracting from the natural staging rather than adding. Perhaps some current 770W system owners could comment on this aspect?