To solve this, many people end up getting a 2nd UPS, in what I call double double redundancy. While UPS failures are rare they do happen. But instead of buying a 2nd UPS, why not consider an Automatic transfer switch? These switches made by APC transfer power nearly instantly to another source. If source 1 fails, power is taken from source 2.
Kit8 includes a splitter dongle that plugs into your outlet and gives source 1 and source 2 from the same outlet. Then the UPS is installed into source 1's path. The transfer switch connects to the UPS's output and connects to the dongle to pickup source 2. Out of the transfer switch is a PDU with all your equipment.
Under normal operation power flows through the outlet, through source 1's path, into the UPS and then out of the UPS through the transfer switch . Our of the transfer switch and to your PDU. If the UPS fails, the transfer switches disconnects source 1 and goes to source 2 directly from the outlet and through to your equipment. If the house power fails, your UPS switches on and still provides the normal backup power through the transfer switch and on to the PDU.
Our plug and play Kit8 allows this to occur at a fraction of the cost of a 2nd UPS. A high voltage Kit8 with dongle, transfer switch and basic PDU costs $375.00