Stroller Triple models are few and far between.  You can choose between Mountain Buggy and Baby Jogger.  Both Baby Jogger models are suitable for running.

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Bebelove Triple USA	Baby Jogger Summit 360 Triple	Mountain Buggy Urban Triple
$449.99	$999.99	$1,099.00
- suspension gives smooth ride - front fixed wheels ideal for runs	- holds up to 125 lbs - easy clean removable fabrics - suspension gives smooth ride - front wheels lock for running	- large underseat storage basket - near flat recline seats for babies - roomy cabin for each child - not recommended for running
- padded, reclining seat	- padded, reclining seats	- padded, reclining seats
- multi-position canopy	- individually adjust canopies	- single adjust canopy
- 2 hand brakes, parking brake	- rear parking brake	- park brake
- adjustable height handlebar	- fixed height handlebar	- adjustable height handlebar
-16" fixed fronts, 16" rear - steel wheels	-12" swivel fronts, 16" rear - front wheel swivel lock - polymer wheels	-12" swivel fronts, 12 rear - alloy wheels
- steel frame	- aluminum frame	- aluminum frame