That's the admitted upgrade path:

So staying within the HPE IMC 7.3 Platform version and updating from E0506 to E0710 should be a matter of checking first if underlying OS+DB supported on E0506 are still supported when you move to E0710...but you question is very reasonable since the update step 7.3 E05xx -> 7.3 E07xx is not a particularly tiny one.
I would check also enabled modules to see compatibility (since you have to update them too once the Platform is updated, if I recall it correctly), avoiding a scenario where those modules (their versions) lock your update process in a "no-go" corner.
Also in Release Notes there is the 6th and 16th sections respectively about "Installing and Upgrading IMC" and "Known Problems" which could be useful to understand issues in moving from the 7.3 E05xx.
Original Message:
Sent: Nov 30, 2023 08:39 AM
From: Spiterman
Subject: HPE iMC Upgrade path from iMC PLAT 7.3 (E0506P03) to iMC PLAT 7.3 (E0710)
Hello,
Does anyone know what the upgrade path is for HPE iMC PLAT 7.3 (E0506P03) to iMC PLAT 7.3 E0710?
I haven not been able to find documentation for this within the HPE support website.
It would be ideal to upgrade directly from 7.3 E0506P03 >> 7.3 E0710, but I am not certain if that is possible or if we need to upgrade to the next available major release from E0506P03 until we get to E0710.
Thanks in advance!