Converting serice Providers

I am looking for methods to convert service providers. We have many servers in a DMZ currently connected to the internet through service provider A IP Subnet and need to convert to Service provider B IP addressing. We need to use the same DMZ ip addressing for this conversion. Current provider travels through a Cisco PIX and the new provider will travel through a Cisco ASA. Question: how can I run both firewalls to the same DMZ?