Yes, it is possible.
There are at least two ways to do it:
- Easiest: Add an extra virtual disk.
- Grow the VMDK and do some arcane SCSI rescan magic followed by increasing the filesystem.
Personally I always used option 1. Both because it is the easiest way and because it allows me to keep a few partitions (such as /home/, /usr/local/, ...) on a separate VMDK 'disk'.
Option 1 is trivial if you use vmware workstation. You can download it for free and use it up to 30 days (trial).
An other way is to manually edit the config files and somehwo create a second .vmdk file. For the configuration changes look at the .vmx file. You want to add lines similar to these:
ide0:1.present = "TRUE"
ide0:1.fileName = "My_new_extra_disk.vmdk"
You should already have at least one entry for a disk. You can just copy that and slightly change it. (If emulation is set to SCSI, just copy the SCSI disk part).
To create the vmdk either copy an already exiting file, or reate a new one (e.g with vmware workstation or oracle virtual box).