Alexi's questline:
(1) Meet him for the first time at the Coliseum [Compete in the arena]
(2) Talk to him again afterwards at the Coliseum [Talk to Alexi]
(3) Encounter and help him at the Construction site [Talk to Alexi]
(4) Encounter and talk to him at the Mages' Guild [Approach Alexi]
(5) Go on a Quest with him at the Adventurers' Guild [Third Quest: Alexi]
(6) See him at the Port (Brothel) [Entertain a prestigious guest]
Not sure if this helps; let me know :-)