As others have said, it is possible. Before you go too far down that road, though, you must ascertain whether you're booting in BIOS mode with MBR or in EFI mode with GPT. It looks like you're probably BIOS/MBR, unless the Windows partitioning tool is hiding your ESP. To be 100% sure, check this page of mine, which presents more details on boot modes. Which boot mode you're using determine which boot loader options are available to you -- and as others have said, the partition table type determines what limits you have on number of partitions.
Beyond that, I must advise against booting more than a couple of OSes directly on a computer. Whether in BIOS or EFI, multi-booting creates complications on the boot process, and those can be difficult to overcome unless you're an expert on the subject. It gets harder the more OSes you add. It's often possible to stumble through it by following a well-written guide or by sheer dumb luck, but a better option is often virtualization. Pick your most important OS (or maybe two) and run it natively, then run everything else in virtual machines. This simplifies each OS's boot setup, and you can even mix-and-match BIOS vs. EFI boots. Personally, I mostly use VirtualBox in Linux, but others like VMware, KVM/QEMU, or other tools.