book (one) through
To reserve a spot on a mode of transportation, such as a train or plane, for someone traveling to a particular destination (perhaps with several connections along the way). Sir, I can book you through to Paris from here. I wish they hadn't booked us through to JFK—their international terminal is always packed. I can book you through to Phoenix, sure, but it's still going to be a two-hour drive to Sedona.
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