Can I create VPN tunnels to multiple peers that use the same internal subnet?

I am wondering if I can create site-to-site VPN tunnels to multiple vendors who use the same internal subnets. I can get either of these two vendors to establish a VPN tunnel and pass traffic independently, but NOT at the same time. When I have them added to the config at the same time, only one of them works. I am using a Cisco PIX 515 running IOS v6.3 and a snippet of the interesting bits is attached.
Thanks in advance!

Code Snippet:

      
        
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          access-list NoNAT permit ip 10.1.0.0 255.255.0.0 192.168.1.0 255.255.255.0 

access-list 91 permit ip 10.1.0.0 255.255.0.0 192.168.1.0 255.255.255.0
access-list 92 permit ip 10.1.0.0 255.255.0.0 192.168.1.0 255.255.255.0

crypto ipsec transform-set strong-des esp-3des esp-sha-hmac 

crypto map partner-map 1 ipsec-isakmp
crypto map partner-map 1 match address 91
crypto map partner-map 1 set peer [ACME Widgets Peer IP]
crypto map partner-map 1 set transform-set strong-des

crypto map partner-map 2 ipsec-isakmp
crypto map partner-map 2 match address 92
crypto map partner-map 2 set peer [Speedy Printing Peer IP]
crypto map partner-map 2 set transform-set strong-des

isakmp key ******** address [ACME Widgets Peer IP] netmask 255.255.255.255 
isakmp key ******** address [Speedy Printing Peer IP] netmask 255.255.255.255

        
      