Nothing as simple as tee, but I was recently at a conference where a new (as in kernel 4.9+ only) kernel probing framework was demonstrated. The presenter has for example a tool that is used to snoop another tty. Everything displayed on the target was replicated on the snooper.
Used eBPF to inject a kprobe - needs pyhon/lua code to inject c code for the intercept and knowledge of the (kernel) function being probed and its parameters. Not simple, but probably a template for what you are planning.
The video of the presentation is
here. He should have links at the end, but
this is the home page of bcc, the userspace compiler collection that takes that python/lua and generates the probe for you.
Have fun - I have.