In every NG cycle, the limit to which equipment can be upgraded goes up by 5
The upgrade path is linear and goes like "Mk. I > Mk. II > Mk. III > Mk. IV > Mk. V" and so on. Mk. I to IV require upgrade materials that also go from I to IV, and a special upgrade material called a "Nanocore" to upgrade to Mk. V.
NG cycles increase the upgrade threshold by 5 up to a maximum of Mk. XX in NG+3.
Because the game only allows equipment to be upgraded to Mk. XX in NG+3, there logically shouldn't be a reason for upgrades to go any higher. However, in NG+4 and up, it seems the game is attempting to increase the upgrade threshold (this can be seen in various Mk. 21 to 24 component drops as well as the schematics being increased to Mk. 21 to 24 in the "Crafting" tab of the Gear Assembly), and this causes the game to immediately crash when attempting to enter the "Upgrade" tab of the Gear Assembly.