So if I'm understanding correctly, Multiplexer is sort of a cross between a hardware multiplexer, a load balancer, and a ghost node.

A sender wants to send payments to a recipient. The recipient has multiple nodes they can receive payment to. The multiplexer generates an invoice with route hints to itself. The route hints point to each of the recipients nodes. The sender tries one route hint (one node) at a time until the payment succeeds. This way the payment is more reliable due to the backup nodes.

When one of the recipient's nodes detects that payment to the multiplexer, the node gets the preimage from the multiplexer and the multiplexor marks the invoice as paid.

If I understand this correctly, this is a pretty cool idea. I can see merchants having this set up so that payments to them are more reliable.