If the cartel records your spends offchain, then you can spend them again onchain to non-cartel merchants. The Bitcoin money supply would be in effect doubled, tripled, quadrupled, depending how many separate cartels do this.
I'm not sure you understand off-chain transactions.
Lets interperate your sentence using what we have today:
1) I have bitcoins on MtGox.
2) I spend these bitcoins by sending them to another MtGox user or to MtGox themselves. Lets say to buy a MtGox T-Shirt. This transaction is recorded centrally on their systems.
3) I now send these bitcoins again (wat), but now using the blockchain. I send them to Bitstamp.
How?