SPECTER, TRUMP and LILIUM form the Sophie Trilogy.
Grand Guignol, COCOON -Dark of the Moon- and COCOON -Upon one of the Star- form the Delico Triology.
In what order should I watch the series?
Suemitsu recommends watching it in the order of release:
TRUMP → LILIUM → Nirin Zaki → SPECTER → Grand Guignol → MARIGOLD → COCOON → Kuro Sekai
Alternatively, you can watch it chronologically:
VERACHICCA → MARIONETTE HOTEL → SPECTER → Grand Guignol → COCOON -Dark of the Moon- → COCOON -Upon one of the Star- → TRUMP → MARIGOLD → Nirin Zaki → LILIUM → Kuro Sekai