can I combine SSH multiplexing with ProxyJump or ProxyCommand (aka 'bastion') forwarding?

Question

I've got a reasonably standard jump/bastion host setup, where I have to SSH from A into C, via B :

Host A --> Host B --> Host C

I've gotten SSH multiplexing set up, which dramatically reduces the time it takes to open a subsequent session from A->B: it cuts this from ~2.5sec down to less than 0.5sec. Is there a way to extend this multiplexing such that I can get the benefits for BOTH hops?

I've tried putting the equivalent ControlMaster and ControlPersist stanzas in the ssh config file on host B, but this didn't help. It's not clear to me that it SHOULD help, as I can't figure out whether the intermediate host actually launches a new SSH session or merely carries the data somewhat transparently?

Current .ssh/config file looks something like this:

Host C
        User myname
        ControlMaster auto
        ControlPath ~/.ssh/sockets/%r@%h-%p
        ControlPersist 3600
        ProxyJump myname@HOST_B_IP_ADDR:22
        LogLevel ERROR