I'm assuming your tanked heater is set to 140F because that is CDC guidance on preventing legionella and other bacteria from growing in the heater. Also, raising storage temp is the first thing you do when trying to extend runtimes.
But that increases risk of scalding which calls for thermostatic faucets. Turning the heat down to protect babies from scalding will shorten shower runtime, but it will also raise legionella, and babies don't like that either.
How it's going to work
OK, so your tanked heater gives you 4 phases of hot water:
- phase 1, AMBIENT (say 70F). The supply pipe had hot water in it some hours ago, but it has cooled down to ambient temp of whatever you heat the building. This "plug" of cool water must be pushed out of the pipe before hot water will arrive.
- phase 2, HOT (say 140). Now the water heater is working as-designed. This is the part of the cycle you actually use.
- phase 3, TEPID (say 90). the water heater is near exhaustion, and the remaining hot water is mixing with new cold water being introduced from the street/well.
- phase 4, AMBIENT (say 70). It's cold 50F water from the street, with the water heater putting its available 23A into heating it, which gives about the same rise as the tankless, giving 70F. Too little.
So let's put a tankless heater downline of this. Let's say at your flow rates, the tankless is big enough to give us a 20 degree rise, and has a shutoff at 110F because with tankless, there's no worry of legionella and other bacteria. So what do we get?
- In phase 1, the tankless warms the "ambient" water to "tepid". :b
- in phase 2, the tankless shuts off entirely. The incoming water is above its set point.
- in phase 3, the tankless warms the tepid water to a useful 120F, but this isn't for very long. And it's useless anyway, since the mix is getting colder and colder, and you're constantly having to adjust the manual knobs. This is no better than it was before.
- In phase 4, the tankless is back to "tepid".
So as you can see, the tankless contributes nothing except adding a few seconds in phase 3, which is a fairly short phase as the tanked heater runs out.
Not what you were expecting
You are imagining that you can extend the tanked heater's time by mixing its 140F water with 45F street water, giving 85F water which you deliver to the tankless. Then, the tankless raises it the last 25F, giving you 110F water at the tap. Sure, that plan will give you hot water for a lot longer time. But you'd have to install special equipment to do exactly that.
Now you are reluctant to simply install mixing valves at your various points of use, so I have to wonder what you are expecting to accomplish on such a low budget.
Keep in mind the way tanked heaters work
A tanked heater is designed to have the absolute minimum possible mixing in the tank. As the tank is used, hot water moves upward in the tank "like a piston" with cold filling the bottom of the tank. That's how it works through the long phase 2.
After most of the hot water is used up, the "piston" of hot water is too thin to remain cohesive, and it starts to inter-mix with the cold. That's when you enter phase 3, the flow turns tepid, and gets colder as the layers mix more.
You shut off usage since tepid water does not satisfy. And then over the next 30-60 minutes depending on sizing, the heating elements go to work to raise the tank of water to target temperature so you can start the process again.
That means putting a tankless on the input of a tanked water heater is also of little value. The tanked heater is doing its best to keep hot from cold separated; changing the "cold" to "cool" does nothing in phase 2 and very little in phase 3.
The right way to use tankless
To make tankless work for Americans, you either need a really, really big tankless coming off 400A service... or you need to combine 2 things:
- A low-flow shower head or other restriction so people cannot out-draw the supply, and
- A tankless heater that is large enough for the planned flow, yet supportable with available electric service.
That is why 30A "electric showers" work in the UK; they restrict flow to where the 30A heater can keep up, and they do it all in a single package.
If you prefer your old legacy high-flow showers and faucets, the consequence of your choice is that tankless will not work for you unless you can greatly upsize your service. Your better plan might be a second tanked heater. But the thermostatic valve situation still needs to be sorted out.
Tankless doesn't store hot water so it doesn't have a legionella problem.