I dont think this is a limitation of SharePoint. Outlook has a 100 recipient per
message limit. If this is something you would be doing often, you should place
the 168 users in mail-enabled security group, place the group in the site
permissions and remove the individual acounts. This way when you use the send
email it will only count as one recipient instead of 168. You may have to create
multiple groups if all of them dont have the same permissions, but you get the
idea...

Why don't you add all these users to a group and then assign this group to
send email?