Disclaimer - I'm not a plumber or heating engineer, just someone with an "engineering mind" and some DIY experience ...
My needs/demands seem to be getting lost a bit, somewhat like Chinese whispers.
Can I just outline what they are again so that we are all clear?
...
So in essence four people need to shower in two sets all in a short period of time during which a sink will need to be used as well.
It would be nice to run three showers (plus sink) at the same time BUT if this is going to cause a disproportionate rise in cost, complexity and space needed then I might leave that alone.
Since all the options revolve around stored hot water, there is (for heat calculations) no limit to how fast you can draw that off. So it's not a huge difference whether you run 2, 3, or 4 showers at once. What it does make a big difference to is the required flow rate - which impacts heavily on the amount of water you'll need to store, and the size of pipework and pumps.
So to support more simultaneous showers, it's
just a matter of more hot and cold water storage (bigger buffer tank), and larger pipes and pumps to handle the flow rate.
Cold storage requirements are relatively easy to work out. Take what you are going to use, subtract how much you'll get from the mains while you are using it, and the difference is what you need to store. Keep it simple, assume 20l/m showers, and 20l/m from the mains.
Running 2 shores, your deficit is 20l/min, or over 15 minutes, that's 300l. During the 15 minute break, you'd replace that 300l - so only 300l storage required (plus a bit !).
Run 4 showers at once, that's 60l/m deficit, or 900l during the 15 minutes of use. So you need to store at least 900l of water, and it will take 45 minutes to refill.
Remember that you need to use total shower flow rate since the stored hot water will be supplying the cold feed requirement of the showers
and replenishing the water drawn from the hot water storage.
Now, as to the heat requirements, if you draw off the hot water "slowly" (only 2 showers, then a break, then 2 more), the heat source can be putting heat back in during that time. In your stated usage pattern, the showers will take around 45 minutes start to end - so you have 45 minutes of heat input which can offset a requirement for stored water.
Draw the same quantity of hot water off in 15 minute (ie 4 simultaneous showers), then you only have 15 minutes worth of heat input while you are drawing off. So you need to increase the stored hot water by the equivalent of 30 minutes worth of what your heat input can provide.
So, very, very roughly, lets say your boiler will take 90 minutes to put back all the heat you've taken out. In the "2 + gap + 2" scenario, half of the heat will have been put in while you are drawing off. In effect you only have to store half of the heat you are using. In the "4 at once" scenario, only 1/6 of the heat will be put back while you are using it, so you need to store 5/6 of the heat you are using.
In the latter case, you need to store 5/6 instead of 1/2 (3/6) - the difference is 2/6, or 66% more than if you spread the showers. But that really is "just" a matter of larger cylinders. In practice, I think the difference in design would be to assume that in the rapid drawoff scenario you'd size the storage to supply all the demand (ie ignore the 1/6 theoretical reheat input), while in the slower drawoff you'd size the storage on the assumption that you'd have some effective reheat (theoretically about 1/2) during use and so could size less storage.
As I say, that's only a very very rough approximation since you won't end up with the cylinder with a clean division between hot water at the top and cold in the bottom. Depending on the specifics of the design, you'll end up with cylinders with varying temperatures - with "bottom up" reheat, you end up with a cylinder full of lukewarm water which isn't useful until it's fully recovered. The above figures assume a "perfect" cylinder where you'll get hot water out until the last drop - imagine a cylinder with hot in the top, cold in the bottom, and a distinct boundary where hot and cold meet but don't mix (they don't generally exist).
This is where the design is critical. I think someone earlier mentioned twin coils - that would allow the reheat to initially work in the top of the cylinder to keep a ready supply of hot water (but not a huge volume), and then switch to reheating the lower part of the cylinder. That can significantly decrease the perceived reheat time by keeping hot water available even though the cylinder has a lot of cold water in the bottom. I can think of a case for using a much larger coil running top-bottom (like the DHW coil in a thermal store in reverse) with the flow regulated to match the boiler output - would give top-down reheat and also extract 100% of the boiler capacity until the cylinder bottom reaches a certain temperature when transfer would start to drop off. Previously I've seen a suggestion to use a combi and reheat the cylinder with the DHW connections of that.
Lots of options, and it needs someone who understands them and can choose the best - rather than someone who will recommend "what he knows".
I hope that's given you some idea of the issues that need to be taken into account.
The price of underestimating is that you spend a lot of money on something that disappoints - perhaps the second set of users find the showers don't run as long as they'd like before running out of heat. Correcting that could be more costly than the initial install, and if you don't have the room (eg for bigger tanks) could be very difficult.
If you overestimate requirements, you pay a little extra (eg for bigger tanks etc), and potentially a bit more in standing heat losses - but this will be nothing compared to the cost of getting it wrong the other way.
