How are S/MIME private keys handled across MUAs?

[vaibhav singh <[e-mail]>]

Hi,
I was looking at RFCs for S/MIME, and had a question: What if I am logged
into multiple clients(my mobile, a web application, Thunderbird) with an
email account, and I receive an encrypted email?

I can see that the encrypted email would be created with my public key,
and, assuming one public key for one email account, I will have one private
key which I will somehow make use of across all my MUAs. I could not think
of a simple way using which I will be able to sync my private key.

Is there any good way of sharing private keys across clients (maybe some
way of securely syncing files)? How do corporate clients resolve this
issue? Is there an RFC which I may have to refer to?

Another line of thinking; is it possible to create key pairs
(triplets?quadruplets?) wherein there could be multiple private keys
generated for a single public key? And, what about the other way round?

-- 

Regards,
Vaibhav Singh