Yes, you may install a 2.5" SATA SSD up to 4 TB, such as this compatible Crucial 4 TB SSD. (That's the model that I have in my L502x, though I chose 1 TB.) I have almost the same laptop as you, since I have the 15" version L502x. With an i7 processor, and now with 16 GB RAM and an SSD, it still works very well. Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard. (Repeatedly touching a metal case part is not sufficient mitigation with modern components.) You should be able to free up space on your current drive with the following steps: go to Settings | System | Storage, and click Show more categories. That will show you what is using the most space. On that same panel you can also run Storage Sense to delete temp files, etc, and you may configure Storage Sense to run automatically in future. Also, do this: That should free up a fair bit of space for you. Note that applications are by default installed to your C: drive. Some applications take up a lot of storage. If there are any applications that you no longer need, you may uninstall them to free up space.
Dear XPS Community May I ask, if it were possible to upgrade this discontinued PC with a 4 Terabyte (TB) Solid State Drive (SSD)? It has been a while since I heard that my PC had been limited to just capable of running a 2TB, which is what I have already upgraded to. I also upgraded the RAM to the Max 16GB. Has anyone experience with this matter, please lend me your wisdom on this. The thing is that I am still studying and I don't think I have enough space to run a few Windows and Linux Virtual Machines (VMs). I can honestly say that this PC has been a joy and it has been my rock. I not to long ago had Win11 in a VM, but I was away and for some reason or another, my hardrive is almost full. I don't need more tools, just VM space.   
Can A 4TB SSD be Installed