I've done my core certified user certification and have good knowledge of fundamentals 2 as well. Does splunk allows to attend training for ITSI without having other certifications?
The ITSI User class (https://www.splunk.com/en_us/training/courses/using-splunk-it-service-intelligence.html) requires fundamentals 1 & 2, so you're fine there.
The Implementing ITSI class (https://www.splunk.com/en_us/training/courses/implementing-splunk-it-service-intelligence.html) adds the Splunk System and Data Administration pre-requisites. You'd struggle in the implementing class--recommend taking the admin courses first.