How to generate a CSR using an existing keypair depends largely on the software you are using. There is however technically speaking no reason it should not work. May I ask why you want to reuse the same keypair for all certificates?
With openssl you can specify which private key to use so if you generate a private key one and use the same private key for all CSR requests then all requests will use the same keypair.
openssl req -new -key privkey.pem
It might be that the CA however does not allow keypairs to be reused. For example EJBCA has the option 'Enforce unique public keys' which only allows a key to be reused for the same person.
Whether or not you get into problems reusing a private key for different certificates depends on how you are going to use the certificates. Most (if not all) S/MIME clients search for the private key to decrypt with using the issuer/serial number pair. In other words, even though the private keys of the certificates are the same, you cannot decrypt the email with for example Outlook if you use the certificate of someone else (in principle it should be possible since the private key is the same, but since the serial number is different, Outlook won't find the correct certificate).
Security wise, it might not be the best decision to reuse the private key (if one certificate must be revoked you need to revoke them all). Whether or not it will work, depends on your use case.