saddle with

: a girthed usually padded and leather-covered seat for the rider of an animal (such as a horse)

: a part of a driving harness comparable to a saddle that is used to keep the breeching in place

: a seat to be straddled by the rider of a vehicle (such as a bicycle)

: to put a saddle on

: to place under a burden or encumbrance

: to place (an onerous responsibility) on a person or group