There are multiple battery options, but there are also cases where the chassis limits the battery size on certain models.  Use your service tag to look up the compatible batteries at parts-people.com.

Some systems have molded-in dividers that will block the installation of a larger battery.  If that's the case, internal modification to the system will be need (sharp knife or a rotary cutting tool like a Dremel).

https://www.dell.com/support/manuals/en-us/latitude-14-7410-2-in-1-laptop/lati_7410_ss/battery?guid=guid-3a48f120-f794-44a7-9f8e-6ca67374e938&lang=en-us

A quick mockup - it seems some hacking would be required. Would the charger or the motherboard present an issue when installing a larger battery, other than the physical fitment of the piece?

The mainboard and power adapter will work fine, though of course it'll take longer to charge the larger battery.

It looks like you need to replace the palmrest assembly to fit the larger battery.

https://www.parts-people.com/index.php?action=item&id=35440

https://www.parts-people.com/index.php?action=item&id=33836

@PatricioMarino​ Please keep this thread updated, I am quite interested. 

Here in India we have small repair shops who can make custom sized larger capacity batteries. I haven't tried this on a Notebook yet. Worked fine on a cell phone. 

Hi

I've ordered the 52 W/h battery in the end, as I could not get the palmrest in black. I still would have had doubts about the placement of the speakers.

The new battery arrives on Tuesday so I'll report if there's any issues with that change and close the thread then. Thanks @enj63 for your help so far!

I've never seen a Dell battery that varies only by thickness, only by height/width profile. If the larger batteries are in fact thicker, that kind of capacity difference should be visible by pictures off Ebay in height. Given they want to make the fewest different parts possible for different configs like this, I'd bet the palmrest is the same for all capacities. Again, stuff like this where there's no info I've been able to pretty quickly figure out just by looking at pictures as it'll be pretty obvious if something won't fit,