If you don't want to buy new higher capacity hard disks and transfer the contents of several smaller (older) drives across, you can install as many hard disks as your computer case will hold. When you run out of motherboard SATA ports, fit a PCIe controller card.
You can disconnect and remove hard disks (and store them in ESD bags) for as long as you like (within reason) then reconnect them to access the data. Alternatively, just leave the drives running in the computer.
I have a couple of Lian Li V2000 cases with room for twelve 3.5in drives each in separate compartments below the motherboard area. When I run out of room on a hard disk, I install another one.
I have 8 SAS hard disks running on an LSI controller card in TrueNAS Core RAID-Z2 system, with two more drives for different OS.
It's not a bad idea to upgrade your system with new storage drives every now and then. Hard drives and SSDs can drop dead at any time. Don't trust all your data to one big drive. Make regular backups on other media.