Creativity with Angle Stop Valve

[scalh001]

I have a 1/4" plastic water line that I want to connect to my cold water supply under the kitchen sink, which is currently fitted with a 1/2" FIP x 3/8" O.D. x 3/8" O.D. Angle Stop Valve to a copper supply line, and run to my refrigerator. I want to focus on a valve solution since I plan to replace cold and hot supply valves anyway.

I know there is probably not a 1/2" FIP x 3/8" O.D. x 3/8" O.D. x 1/4" O.D.--which such a beast would be too good to be true. However, I need to turn this into a 4-way valve.

I already purchased a water line installation kit, but do not want to use a Self-piercing T-valve because it can easily leak, and I worry that it might not work with code in my area. Not to mention, I would have to bust into wall nearby to find exposed copper pipe, and there is not enough exposed pipe under sink.

What is the most practical way to connect this 1/4" water line to my cold water supply (sink is nearest connection), without having to solder anything? Will it require me to somehow branch from one of the 3/8" O.D. outlets?

Lend your expertise to DIY project please.

 

[Caduceus]

The result may look like an experiment-in-plumbing-gone-wrong, but maybe this will help. Out of the new 1/2" x 3/8" x 3/8" dual supply valve you could connect a 3/8" compression tee via 3/8" copper or 3/8" fem no-burst connection. The other connection from the dual valve will go directly to the sink faucet.
Out of the compression tee, another short cooper or no-burst and a 3/8" x 1/4" compression reducer coupling. This will leave you with a 3/8" and a 1/4" compression connection at the end of the tee.

You had mentioned that you were concerned with code in your area. As a note to that subject, dual valves are against code in most areas anyways. Each appliance and fixture is required to have its own individual shut off valve. But as you have stated, there is no room unless you cut the wall open to expose more copper pipe. As a DIY project my advice may be a solution, but is not the preferred or recommended method of solving the problem by professional plumbers.
So, to recap.
1. Dual valve supply to sink faucet from one port.
2. Remaining port to 3/8" tee.
3. Reduce one side of 3/8" tee to 1/4"
4. Result should be three 3/8" connections and one 1/4" connection.