If you want exim to accept email for a set of domains and then forward those emails onto their main mailserver later on, then you can do so by using the following guide:
1) create /etc/virtual/mx_domains. Fill it with all domains that you want to have relayed. Note, the domains should not exist in /etc/virtual/domains, as that would be a contractiction as to what you want to do. Chown it to mail:mail
2) edit your /etc/exim.conf, find the code:
domainlist relay_domains = lsearch;/etc/virtual/domains : localhost
Change it to show:
domainlist relay_domains = lsearch;/etc/virtual/domains : localhost : lsearch;/etc/virtual/mx_domains
save, exit and restart exim.
Just as a warning, any spam sent here that is either a non-existant account or flagged to be bounced will be sent back to the sender, even if that sender address is spoofed (faked). Just keep in mind of the possible spam/load increases if this option is used.