Scripts within Scripts I have read the following: 

https://github.com/bitcoin/bips/blob/master/bip-0016.mediawiki

https://darkwallet.is/bip16-17

However, I would like to know, can one specify a pay-to-script hash that includes another pay-to-script hash? 

E.G. 

Script for payer: 
DUP HASH160  EQUALVERIFY CHECKSIG

scriptA: 
DUP HASH160  EQUALVERIFY CHECKSIG

Can one include a CHECKSIG operation for another script inside a script referred to by a pay-to-script hash? 

I'm probably not communicating this clearly, but I would basically like to know whether I can "daisy-chain" pay-to-script hashes together. 
Let me know if I should add more examples, or what changes I should make to this.
No.

BIP-16 says that client executes script and if it matches P2SH - removes top item from the stack and executes it as script. That's all. No inner loops and checks.