The T-k1 might be a single point of use commercial apps unit. That could be the problem.

Quote from Takagi on the t-k1s:

'Designed for single-use commercial applications, the T-K1S provides 190,000 BTUs of continuous heat'.

The unit i was looking at was the T-KD20 which is similar to the T-K2 with the exception that the T-KD20 has duel vents; the second vent is to bring outside air into the heater for combustion.

I live near Milwaukee Wisconsin and the ground water is 50f. With a 50 degree rise, the Takagi T-KD20 will provide 6gpm. With a 70f rise, the GPM is 4.5 GPM. For 40F ground water you are looking at just over 5GPM for 100F water output and about 3.8 GPM for 120F water.
After researching a lot i decided to settle on the Rinnai Continum 2532 because it is stated to provide more GPM than the Takagi with same temp rise. There are some other reasons too.
The Rinnai clearly state on their web-site that it a multiple point of use heater. The Takagi is also made for multiple point of use.If you look at their graph of GPM vs Temp Rise will tell you how many fixtures/showers you can run simultaneously and get the GPM you desire.
Yes you can run 2 or 3 showers at once with a tank water heater but they will be very short showers and you have to wait for over 30 mins to get hot water again. Comparing the GPM follow of a Tank type and Tankless is like comparing apples and oranges.

Just an example:You can get 50 GPM from a Tank (hypothetically) but if its a 75 gallon tank well in less than 1.5 minutes you are out of hot water.

GPM usage is depended on the appropriate Temperature Rise/ output you desire.
You can't expect to get 120f Water (with below 50f ground water) and still run 2 3.5 GPM showers.
Setting the max temp on your Heaters to the lowest temp you need will also increase GPM and efficiency.

Tankless are really the future and its suprising why people here still use Tanks; its obsolete technology.
When I lived in England, I had a Paloma (Italian) Tankless water heater and I had no problem running a shower and a faucet at the same time and still got hot water from my English 5GPM shower head.
Tankless water heaters are in my opinion hands down superior to Tank types. The initial time delay is insignificant.
If you have a Takagi T-K jnr then you are not going to be able to run 2 showers. The rinnai 2532 and the Takagi T-kd20 should be adequate. Both these models are for 2+ bathroom households with washers.