Dear Victoria, thank you for your kind suggestions.
However, when I change the .htaccess file adding any of the lines described, it causes Internal Server Error when reloading our website. Changing the values to 512M and 256M respectively in the default-constants.php only does not have any effect. Where should be the lines placed exactly in the .htaccess file? Our .htaccess file looks like this:

# htaccess rules for subdomains and aliases
# to create new subdomain, create a folder www/subdom/(subdomain name)
# to create web for alias, create a folder www/domains/(whole domain name)

# htaccess pravidla pro subdomeny a samostatne weby aliasu
# pro vytvoreni subdomeny vytvorte adresar www/subdom/(nazev subdomeny)
# pro vytvoreni webu pro alias vytvorte adresar www/domains/(cely domenovy nazev)
# dalsi info a priklady: http://kb.wedos.com/r/32/webhosting-htaccess.html

RewriteEngine On

# cele domeny (aliasy)
RewriteCond %{REQUEST_URI} !^domains/
RewriteCond %{REQUEST_URI} !^/domains/
RewriteCond %{HTTP_HOST} ^(www\.)?(.*)$
RewriteCond %{DOCUMENT_ROOT}/domains/%2 -d
RewriteRule (.*) domains/%2/$1 [DPI]

# subdomeny (s nebo bez www na zacatku)
RewriteCond %{REQUEST_URI} !^subdom/
RewriteCond %{REQUEST_URI} !^/subdom/
RewriteCond %{HTTP_HOST} ^(www\.)?(.*)\.([^\.]*)\.([^\.]*)$
RewriteCond %{DOCUMENT_ROOT}/subdom/%2 -d
RewriteRule (.*) subdom/%2/$1 [DPI]

# aliasy - spravne presmerovani pri chybejicim /
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^domains/[^/]+/(.+[^/])$ /$1/ [R]

# subdomeny - spravne presmerovani pri chybejicim /
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^subdom/[^/]+/(.+[^/])$ /$1/ [R]

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>

# END WordPress 

Thanks Rikard. I tried to deactivate all plugins one-by-one with no result on the issue. Then I tried to deactivate all of them at once, but with no result on the described issue as well.