Imagine I have a single-IC switching DC-DC converter which supports input voltage up to 16V, for example a LM2727.
Can I stack the inputs of such converter in series, for example 64 of them, and be able to apply up to 1024V across the combined input?
I need lots of stable 3.6V outputs anyway (for charging each cell in a multi-cell battery separately).
And on the output side, can I put a 3.6V cell between the outputs of each DC-DC converter and then connect all the batteries in series – will that be fine, or everything will blow-up?
Connecting the chargers in series
Connecting several such switchers in series will be a problem since they would have to share the same supply current (all would have to draw the same current all the time). All the chargers have some input resistance which vary according to their immediate needs. If one of the chargers draws less current then:
To verify this logic assume that one charger finished charging and does not need any current at all. The same thing happens.
The only way out is to dissipate excess (unneeded at the moment) power but that is probably not something you would like to do. :)
High input voltage SMPS
A single SMPS supply working from 1000V input is also quite difficult to do since most MOSFETs and IGBTs are only rated up to 1200V. A 600V supply should be doable.
Output current regulation in multiple-output SMPS
You could do a multi-output transformer based switched supply and regulate the output voltages and currents with a magnetic amplifier (this Ferroxcube flyer is a proof that this is used in real circuits)