Yes, you can use a redeemScript that has a lot of OP_CHECKSIGs and boolean operations. You would have to enumerate all possible combinations of signatures however.

As a simple example, if you used a 2-of-2 multisig, traditionally your redeemScript would be

OP_2 <pubkey1> <pubkey2> OP_2 OP_CHECKMULTISIG

and the scriptSig is then

OP_0 <sig1> <sig2> <redeemScript>

Without OP_CHECKMULTISIG, your redeemScript would be

<pubkey1> OP_CHECKSIG OP_SWAP <pubkey2> OP_CHECKSIG OP_BOOLAND

and the scriptSig would be

<sig2> <sig1> <redeemScript>

For more complex multisigs with more keys and m-of-n, the scripts will be much more complicated with more OP_SWAPs, OP_BOOLORs, and OP_BOOLANDs.