There are quite a few functions/features that aren't available yet in the 2H 2023 new Integrated Learning Experience (ILX) homepage and customising the layout is definitely not available at this stage though I do believe that they have custom tiles on the Roadmap for 2H 2024.
Though most functionality is slated for future release on the SAP LMS Roadmap there are still some features that aren't well covered as to when they will be coming (E.g. Assigning Delegate/s, Reporting, My Teams, My Classes, Record Learning History, Record External Training Event, Request External Training etc..).
I'd like to see everyone get together to discuss this so I'm directing people to review and add their feedback on the following post:
I'm especially interested to hear what approach people are going to take with this release (e.g. Opt-In or Opt-Out).
Please go to the above link and leave your thoughts.