I’ve heard of this before, and despite what sailor says, I think it’s the best overall solution in your case. This arrangement allows you to buy a smaller, much cheaper, tankless heater than you would otherwise need while still providing you with the advantages of longer lasting flow of hot water and no temperature variation with changes in water pressure.
I don’t follow the logic. It seems like it would obviate the advantage of the tankless system since the water would be heated and then just sit there, and still be limited by the flow rate that the tankless could heat up from outside pipe cold to acceptable hot after the tank was emptied. I similarly don’t get the idea to recirc the water out of the tank to an external tankless heater and then back into the tank. Okay, both reduce recovery time, just like my idea of using one tank to preheat, but the less energy wasteful way would seem to be to prewarm in the tank and give it the final boost to acceptable hot with tankless on an as needed basis, knowing that the flow rate possible going from warm to hot is much greater than from cold to hot, that the recovery rate from cold to warm is much less than the recovery rate from cold to hot, and that the loss from a tank full of hot water sitting there for many hours (and need to keep heating it) is much greater per unit time than needed to keep a warm tank just sitting there.
What am I missing?
I build infills, and we almost exclusively install high efficiency tankless heaters. We are building one home with a geothermal system currently (nice but a 20000CAD additional expense). Our customers have all been very happy with their tankless systems. Note: these are gas appliances, and we have a long winter and a cool summer here.
Direct venting tankless heaters and high efficiency furnaces eliminate the need for a chimney, and reduce HVAC requirements for make-up air systems. We use the tankless system to heat the basement slab, and we preheat the supply line with the basement slab so that the tankless system needs only raise the water temp a level that is within its best efficiency range. This would keep the supply water a consistent temperature also, (though I would be surprised if there is much since it comes from a reservoir and runs through miles of underground pipe.
For a new home of moderate value I think it is a no-brainer. I dont know if the energy savings are enough to economically justify the extra expense of a tankless system for an existing home. Also tankless systems require regular maintenance.
Just to qualify a bit, I am a licensed plumbing contractor. I’ve got experience with tank-type heaters (both gas and electric) in commercial, industrial and residential applications. I have designed water heating systems for a number of applications.
Regarding this type of installation, in a residential application you have several choices here.
[ol]
[li]Replace the bad tank-type heater with another tank-type heater in parallel. This will essentially leave you in the condition you’re in now, just with 2 working heaters[/li][li]Replace the bad tank-type heater with a tankless heater in parallel. This would be a waste of the heater’s capabilities and would be rather ineffective.[/li][li]Replace the bad tank-type heater with a tankless heater in series with the existing heater. This will work, but is not the most efficient use of the heaters.[/li][li]Replace both tank-type heaters with a tankless heater with enough capacity to handle the potential demand (a 9GPM heater would be overkill).[/li][li]Reconfigure your system to utilize the existing heater as a storage tank with a recirculating pump to keep the tank hot. This is a very efficient system, although it does take a bit of piping and additional cost.[/li][/ol]
Electric tankless heaters in a whole-house application normally require a service upgrade to your home as they take 2 50A circuit breakers and take up a bunch of the capacity in the average home’s electrical panel. This makes them a poor choice for a retrofit, but luckily you’re not dealing with this.
Gas tankless heaters are very efficient and have been in use in Europe for a long time now. They allow you to set a fairly accurate water temperature. The biggest downfall with them is when they are undersized for a particular application, and the installer does not take into account the worst-case scenario for the system. Worst-case is normally in the dead of winter, when the incoming water temperature is at it’s coldest. Tankless heaters put out hot water based on the desired temperature rise, so a heater rated at 6GPM at a 40 degree rise may only put out 3GPM at an 80 degree rise. Where this comes into account is when the incoming water temperature is down to 40 degrees in January and you still want 120 degree hot water. This is where a storage tank with a recirculating pump system is worth the additional cost, since the storage tank will give you a buffer for the reduced efficiency of the heater.
OK, I could go on longer, but I think you get the idea. Feel free to send me a PM or e-mail if you have another question 
I hope this is permitted:
There are several issues at work here, depending on which installation you’re considering. Fluid dynamics, balancing water flow through multiple units and temperature control are all considerations.
The advantage of a tankless water heater is that it only heats water when there is a demand for it. That alleviates the issue of the water heater kicking on & off all night long to keep water hot, and keeping the tank hot the entire time you’re not home. The other advantage is that there’s not a big tank of water sitting in your house, taking up space.
Keeping your existing heater at 100 degrees and using the tankless heater to heat it the extra 20-30 degrees a bad idea from a money standpoint, it’s just wasting the capability of the tankless heater. It’s like using a Corvette as a NYC cab. Sure, it will get you from Battery Park to the Beacon Theater and it will be a nice drive, but you’re not using the capability of the Corvette very well.
If you’re seriously considering keeping the existing tank, just replace the existing tank heater with another one. You’ll spend less money on the replacement, and it will give you decent capacity.
Not long ago, I installed a tankless heater in a customer’s home. He had his wife and 3 daughters between 13 and 16. A few weeks after the installation, he called me to tell me that he had taken 3 weeks of hot showers for the first time in many many years. A 6.3GPM unit was keeping up with the house easily. With you being in Chicago, I would consider a 7.5GPM Noritz unit. That heater alone will keep up with your demand.