As a site admin, you will not be able to install any plugins.
If you find that you would like a plugin for your site, please contact TSG with all the relavent information.
There are a few that will not be permitted due to security or performance related issues.
Here is a relatively short list of disallowed plugins
adminerasync-google-analytics
backup
backup-scheduler
backupwordpress
backwpup
broken-link-checker
contextual-related-posts
duplicator
dynamic-related-posts
ewww-image-optimizer
ezpz-one-click-backup
file-commander
fuzzy-seo-booster
google-xml-sitemaps-with-multisite-support
hc custom wp admin url
hcs.php
hello.php
jr-referrer
missed-schedule
no-revisions
ozh-who-sees-ads
portable-phpmyadmin
quick-cache
seo-alrp
si-captcha-for-wordpress
similar-posts
spyderspanker
spyderspanker_pro
super-post
superslider
text-passwords
the-codetree-backup
toolspack
ToolsPack
tweet-blender
w3-total-cache
wordfence
wordpress-gzip-compression
wp-cache
wp-database-optimizer
wp-db-backup
wp-dbmanager
wp-engine-snapshot
wp-file-cache
wp-mailinglist
wp-missed-schedule
wp-phpmyadmin
wp-postviews
wp-slimstat
wp-super-cache
wp-symposium-alerts
wpengine-migrate
wpengine-snapshot
wponlinebackup
yet-another-featured-posts-plugin
yet-another-related-posts-plugin
The idea here is not to block all plugins, but to maintain the best possible performance for all the sites hosted here.