(privA + privB) + ... + (privY + privZ) --> (pubA + pubB) + ... + (pubY + pubZ)
And does doing so weaken the key strength? Is each component (A,B,C...Z) easier to crack than the additive result, or do they all contain just as many bits and are just as seemingly random?
Each private key can contains as many bits as the unified private key. The entropy of each private key depends on the method used by the creator. Even if one key is weaker due to flawed implementation it is still stronger than a single key because you will need all the sub-keys to construct the unified private key.