Concept of Route Once, Switch Many

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I have a (hopefully) simple question with regards to the concept of
"Route Once, Switch Many" and how it applies in a switched network with
many multilayer switches. Let's say that between a host and a server
there are 4 switches (an access switch, distribution switch, core
switch and another distribution switch). There isn't going to be a
switch that has virtual interfaces on both the host's VLAN and the
server's VLAN, so the traffic will route twice (once from the host's
VLAN to a common VLAN, and then again from the common VLAN to the
server's VLAN). Or am I overthinking this in that the "route once" not
include multilayer switching?

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