"I wonder if you can partition a partition???"
Yes, you can create as many partitions as there are letters in the alphabet, subtracting for any floppy, cd/dvd drives, utility and/or recovery partitions you might have, as well as older mem stick/card readers that assign drive letters to them. There might be a few more exceptions, but I doubt you'll ever reach the end of the alphabet to worry if you have enough letters.
Heres the rub, For more than 3 partitions, you have to create an extended partition. Then from within the extended partition you create logical partitions. You currently have an extended partition, but unfortunately, its only 20 gigs. For you to make more partitions, you would have to delete both windows 7100 & 7260 and then the current extended. With the newly freed 110 gigs, you create an extended partition with all that space, then create logical drives from within the extended. You can create as many as you want with the space you have up to the limit discussed, but doubt you would have to worry about that with 110 gig's.
Since Vista, (as you can see cause you have an OS installed on a Logical partition), its possible to install OS's from Vista and Newer on Logical Drives. With XP and older legacy OS's, they would have to be installed only on primary partitions to which on windows is limited to 3. The forth partition would be the extended, and logical partitions are all that can be created from within an extended partition. You cannot create a primary partition from within an extended partition. Also, You need at least One Primary partition for the boot manager.
Should you decide on redoing your hard drive, I recommend the following:
1. KEEP YOUR HP RECOVERY PARTITION (1st thing to do- If your PC didn't come with recovery disc's, you should be able to create them and suggest you do so. Within your Original OS, should be a program from HP to create them).
2. Your first partition would be a Primary one sized appropriately for how you intend on using it. If your installing Vista and a few programs, but don't really intend on using it too much, then keep it reasonably small. With Vista, somewhere around 24 gig's would be about as small as I would go. Increase if you have a lot of programs to install. Take a look at what you have now, see what you would keep and size appropriately leaving a little "head room" I'd say you want to try and keep about 25% of the partition empty. For disk defrag to run, it needs a minimum of 15% free. But keep in mind you can always reduce the size of the page file, system restore, and the recycle bin to free up space.
3. A> You could create a second primary partition, just to have another primary partition in case its needed in the future, about 24 gigs. You could always use it as storage, untill needed for an OS.
3. B> Create an Extended partition with all remaining space.
4. Create as many Logical partitions as you want, sizing them appropriately for how you intend on using them. (Install Vista and Newer OS's here)
Hope this helps, Oh & btw, theres no such thing as "too much"