REFER
initial-dialog is much cleaner than INVITE of 3PCC, but it's
usually not allowed by common phones. So a PBX or
SIP server implementing click2dial could try first a REFER
initial-request, and in case it receives a negative response (i.e.
"403 Forbidden" or "501 Not Implemented") the the server could use
the
3PCC INVITE.
You can do it with kamailio/openser - uac module first, then dialog
module.
The admin can even build a list of devices supporting first or second
option.