Yes and No.
It's possible to have multiple certs that all have the same domain name on it. You could have a Comodo example.org cert and an Entrust example.org cert, both of them valid and official, no problem. I believe some load balancers will rotate which one is used on a per-connection basis, but only in a round-robin fashion.
The No is that you're asking if you can select which cert to use based on the URI (/ vs. /criticalpath). The problem is, the URI is only available after the SSL connection has been nailed up using one of the two certs. So you can't really choose which cert to use based on information you can only have after you've chosen the cert.
Now, I'm not going to say 100% it's impossible. With Apache, for example, you can set the SSLCipherSuite configuration on a per-directory basis, so I wouldn't be surprised if there was some way to force a renegotiation that would involve a new cert. But I rather suspect it's practically unimplemented even if it is theoretically possible. (Apache SSLCertificate* is per-server or per-vhost, not per-directory).
Appendix: Musings upon renegotiation
Disclaimer: I haven't done any of this, it's a layman's interpretation of the RFCs and other documents. Dozens of people here are far more qualified to comment than I.
I'm going to look at TLS 1.2 since it's neatly described within RFC 5246.
Section 18.104.22.168, "The HelloRequest message MAY be sent by the server at any time." That should trigger the Client to renegotiate the connection. (The client MAY ignore that request, and the server MAY drop the connection if the client ignores the request for too long.)
A renegotiation looks very much like an initial negotiation, although it may pass some information from the previous negotiation forward to try and smooth the path (e.g., here's the cipher we agreed upon last time). So the Client sends a ClientHello, then the server sends a ServerHello, then the server sends a Server Certificate (7.4.2).
So my read of the RFC is that, yes, a server can force renegotiation of a connection, including the selection of a different server certificate.
I'll be honest with you, I don't know that you'll find existing software that will do what you want to do. I would suggest you start playing with Perl Crypto::OpenSSL or Python's ssl lib to see if you can test it out.