I think you might be new with WP Multisite. That is OK. I'm using Multisite for last few years and I really don't know any way to put the different site tables in different database.
The way WP Multisite works is a single WP installation for multiple WP site. Now suppose you have a database called
my_multisite; within this database WordPress will create all the tables. Now if it is a Multisite installation and at the time of installation if you select the table prefix (say
ex_) then your root site tables will be like
ex_blah_blah. Now when you will create another site within that Multisite installation, the prefix value will be incremented by 1 and the new sites will have the same tables with the names like
ex_2_blah_blah. For next site you create it will be
.... There is no way change this pattern.
Trust me this is all right for your site. If you want to have your different site tables to different database, you have to go with multiple WordPress single installations. But Multisite database does not degrade any performance for most of the good hosts. Just make sure you host your site with a legit and good hosting company.