[exim] OT: DKIM - but nothing to do with Exim!

Please forgive asking here, but the advice is always so good.

I'm trying to figure something out with DKIM that is making my head
explode. It's probably so simple too, but do you think I can find an
answer? No.

Suppose I have MTA (Exim/Qmail/Sendmail - doesn't matter) that is shared
amongst multiple domains. A 'main' domain name - say -
'somehosting.null' exists, and signs outbound mail with DKIM using it's
private key. When mail is sent from 'anything@???' DKIM
verification is fine because the domain has suitable DNS records to
authenticate it.

Now, another domain comes on stream with this shared MTA - say
'anotherdomain.null'. How can this ever send mail that is DKIM signed
when the private key is for somehosting.null?

Obviously I'm missing something really obvious here in my understanding.
Can anyone put me out of my misery?

Kind thanks
Ron