They should use multi-button mapping in order to combine the d-pad with other buttons in order to create more options. Essentially, pressing one of the d-pad options would change the functions of the other buttons.
Example: Down on D-Pad switches your controller (while pressed (or have it on toggle)) to emote mode. This makes it so that your R1/R2/etc. buttons now do various emotes such as dancing, waving, bowing, thanking, pointing, etc.
These could either be hard linked or custom linked (custom linking meaning you go to your menu and there is a list of say emotes. You hover over one and then you press the keypad command you want to link it to)
Up on D-Pad could allow you to use items. Again, either hard linked or custom linked.
Left on D-Pad could allow you to swap gear sets (sub class, weapons, armor, and even the subperks of each). Again, hard linked or custom linked and adding gear set functionality
Right on D-Pad could be used for various menu functions like: Open Map (like, with all our technology, we don't even have the ability to see the map (which we can see from the mission select screen I might add) in the game?), Set waypoint (you know, to show your friends where to go), Set priority target (sort of like a point command where it shows text when aiming at someone but for enemies or objects), Toggle objective display (instead of having to open the nav mode and close it over and over again to show.) and so on.