Adding www over .htaccess couses inifinite loop in wpmu

Hi All,
Im having this issue with adding www to a domain name via htaccess since i forgot to do that on single install, now this simple rule causes infinite loop. Here is the htacces (i changed my domain into mysite.com):

# BEGIN W3TC Browser Cache
<IfModule mod_deflate.c>
    <IfModule mod_headers.c>
        Header append Vary User-Agent env=!dont-vary
    </IfModule>
        AddOutputFilterByType DEFLATE text/css text/x-component application/x-javascript application/javascript text/javascript text/x-js text/html text/richtext image/svg+xml text/plain text/xsd text/xsl text/xml image/x-icon application/json
    <IfModule mod_mime.c>
        # DEFLATE by extension
        AddOutputFilter DEFLATE js css htm html xml
    </IfModule>
</IfModule>
# END W3TC Browser Cache

#RewriteEngine On
#redirecting wwwto non-www
#RewriteBase /
#RewriteCond %{HTTP_HOST} ^www.mysite.com [NC]
#RewriteRule ^(.*)$ https://mysite.com/$1 [L,R=301] 

# Redirect non-www urls to www
RewriteEngine on
RewriteCond %{HTTP_HOST} !^www\.mysite\.com
RewriteRule (.*) https://www.mysite.com/$1 [R=301,L] 

#WPMUsetup
RewriteBase /
RewriteRule ^index\.php$ - [L]

# add a trailing slash to /wp-admin
RewriteRule ^([_0-9a-zA-Z-]+/)?wp-admin$ $1wp-admin/ [R=301,L]

RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(wp-(content|admin|includes).*) $2 [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(.*\.php)$ $2 [L]
RewriteRule . index.php [L]

# compress text, html, javascript, css, xml:
AddOutputFilterByType DEFLATE

 text/plain
AddOutputFilterByType DEFLATE text/html
AddOutputFilterByType DEFLATE text/xml
AddOutputFilterByType DEFLATE text/css
AddOutputFilterByType DEFLATE application/xml
AddOutputFilterByType DEFLATE application/xhtml+xml
AddOutputFilterByType DEFLATE application/rss+xml
AddOutputFilterByType DEFLATE application/javascript
AddOutputFilterByType DEFLATE application/x-javascript

# Or, compress certain file types by extension:
<files *.html>
SetOutputFilter DEFLATE
</files>