So each card generates a 1.1 volt supply, and you want to interconnect it between cards so that if power is lost to one of the cards, the other cards will power it?
The forward voltage drop of diodes is obviously a problem at such low voltage. At such low voltages, bipolar transistors can be used to sort of make diodes with no forward voltage drop by biasing the base with sufficient current, and there is probably some way to improve that. This only works at low voltages because the reverse breakdown voltage of the base-emitter junction is only like 5 volts.
1 amp is not all that much. If the 1.1 volt supplies are regulated closely enough, then they can be connected directly in parallel and rough current sharing will be enforced by the series resistance between the sources, or 10s of milliohms of series resistance can be added at each output.
I am dubious about sharing such a low voltage between cards. Better might be to share a slightly higher and not as tightly regulated voltage, and implement 1.1 volt regulation on each card.