You Can Do It!
I actually just did this very thing myself. I installed a new copy of phpmyadmin on a subdomain of my main account. I used the httpsdocs... so I got the SSL connection. I setup phpmyadmin, added an extra user to the database, and then logged into phpmyadmin with admin privs to change user priveledges. Here's a more detailed walkthrough.
1. Download and installed PHPmyadmin.
http://www.phpmyadmin.net/home_page/index.php
Like I said above, I created a subdomain on my main account (phpmyadmin.<mydomain>.com). I then uploaded the phpmyadmin files into the httpsdocs folder.
2. Prepare MySQL
You'll need to log into Plesk and add a new database (you can do it under any domain, but I suggest your domain, not a client's). Call this database anything, like 'phpdb'. This is a database for the new installation of phpmyadmin to store it's settings and such. Also through Plesk, create a standard user for this database (ie, 'phpdb_user').
3. Create a writable folder for phpmyadmin setup
This is easily done through ssh. Log into SSH and browse to var/www/vhosts/<yourdomain>/subdomains/phpmyadmin/httpsdocs (or wherever you installed it).
First you must manually create a folder config in the phpMyAdmin directory. This is a security measure. On a Linux/Unix system you can use the following commands:
mkdir config # create directory for saving
chmod o+rw config # give it world writable permissions
*Don't close your ssh connection, you'll use it again
4. Configure PHPmyadmin
Next, open scripts/setup.php in your browser. Note that changes are not saved to disk until explicitly choose Save from the Configuration area of the screen. Normally the script saves the new config.inc.php to the config/ directory, but if the webserver does not have the proper permissions you may see the error "Cannot load or save configuration."
Continue to add the server to the config file. You don't have to change much. I suggest using cookie authentication. You'll have to enter the database info you created in Plesk a minute ago under the phpmyadmin config db field or something. I forget exactly what its called. If you fail to enter it, it will warn you that it doesn't have a DB for preferences and stuff.
Anyway, once you add the server, you're pretty much done configuring phpmyadmin unless you want to manually change defaults for display and such.
Once the config file has been saved, it must be moved out of the config/ directory and the permissions must be reset, again as a security measure. Do this through SSH:
mv config/config.inc.php . # move file to current directory
chmod o-rw config.inc.php # remove world read and write permissions
5. Change user accounts
You should now be able to login to the new installation of phpmyadmin through any username/password on your server. So, your clients should be able to login and see only their databases... and likewise, you should be able to log in as 'admin' and **** and see ALL databases. Very nice if you're a web developer for these clients.
Anyway, if you login through the admin account for your server, you can add and change user accounts. This includes creating users with limited privs.
Final Comments
As with almost all opensources wonders, there's tons of documentation out there on configuring your own phpmyadmin installation. The downside of this is course that Plesk doesn't interface well with phpmyadmin. Sure, the users and db show up there. However, how is a limited user going to interface with phpmyadmin? If they go through Plesk, there's nothing stopping them from using the account with higher privileges. In other words, Plesk
never requires phpmyadmin users to put their passwords in... it makes you wonder why they even require you to have one (well, it's b/c mysql requires it).
Point is, for you to implement this in a way that an actual user doesn't have the rights at all, they can't go through plesk anyway. But now you've set it up on a sub-domain which makes it darn stinkin' easy to administer. Heck, it's easier to remember than adding port 8443 on the end of the domain!
Good luck and hopefully this is what you were looking for... if not...I may have wasted 2 minutes!
Ciao!