Question about Brother Additional tray LT-340CL / 500 sheets

Hello Mathias
No, this add-on tray "only" fits the following devices: HL-L8360CDW, HL-L9310CDW, MFC-L8900CDW, MFC-L9570CDW, MFC-L9577CDW. A maximum of 2 units per device is possible.
See also here: https://www.brother.de/verbrauchs...

For your DCP-L3550CDW, there are no additional trays as an option.
Another possible combination (apart from the devices suggested above) would be: HL-L8260CDW, DCP-L8410CDW or MFC-L8690CDW with 1 or max. 3 units. LT-330CL.
Greetings