Some manufacturers of external hard drives with capacity exceeding MBR partition capacity seem to sell them pre-partitioned to a 2TiB partition and one with the remaining capacity.
Tools are available to make a single, larger partition out of these (at least I think I learned as much from amazon reviews of such products; presumably the disk is in GPT mode afterwards).
Can I go the other way, i.e. use the full space of a 3TB drive, while at least one partition can be used in MBR mode (for booting Windows in a non-UEFI machine)?
The drive is a 3.5" HD Seagate Barracuda something currently inside a USB 3 box. This Seagate Disk Wizard (pdf) for Windows, which may not be helpful anyway, refuses to install for alleged lack of a Seagate HD. I have a (non-UEFI) PC (with SATA I only) available and would not be afraid to use linux-based tools.
Best Answer
MBR or GPT is the whole disk's format, not a partition, so you cannot have an MBR partition on a GPT disk like that. Hybrid MBR/GPT is a drive with both GPT entries and normal MBR entries, not an MBR partition on GPT disk.
Some manufacturers worked around the problem by partitioning the first 2 TiB as MBR then install Windows normally. After finished installing they install a special driver to make the OS recognize the remaining space as another separate drive so you can utilize all of the available space. This is fragile and not portable so I don't recommend using it this way.
The easiest way is just split the drive into multiple sub-2TiB partitions. Contrary to common beliefs, the limit in MBR isn't 2 TiB but 233 - 2 blocks which is ~4 TiB for normal 512-byte-sector disks and ~16 TiB with 4KB-sector disk (A.K.A Advanced Format) due to the way it defines partitions (offset + length instead of start offset + end offset). You can achieve that by having a single last partition start before the 2 TiB mark. For example with a 3 TB drive you can partition into a 2 TB volume + 1 GB volume (remember 2 TB < 2 TiB), a 1.99 TiB volume + 756 GiB volume, two 1.5 GB volumes, or two 800 GB volumes and a 1.4 TB volume
You'll need OS support for this, and also need a 3rd party disk partitioner instead of diskmgmt.msc. Fortunately Windows 7+ and all modern OSes will work with those disks without problem. To quote from Rod Smith's article above
There are many other ways though. If you use Linux or BSD then you can boot from a GPT disk in BIOS mode easily. Just create a small BIOS boot partition before installing. See Is it possible to boot Linux from a GPT disk on a BIOS system?. In Windows it's a lot trickier because you do need UEFI to boot from GPT disk. Luckily a hardware UEFI isn't required, a software UEFI like DUET or Clover works completely fine, although it's not very easy and will boot a lot slower. If you're really interested in making it work that way then see
Alternatively you can use Grub2 to boot Windows from an ISO or WIM file. This way it boots much faster than a software UEFI solution
Another method is installing Windows on VHD on a GPT disk. Just format the drive as GPT then when installing Windows, press Shift+F10 and create a VHD, mount it and then continue as normal. I haven't tried it but many people have confirmed that it works