Motivated by recent observations of charge order in the pseudogap regime of hole-doped cuprates, we show that {it crisscrossed} stripe order can be stabilized by coherent, momentum-dependent interlayer tunneling, which is known to be present in several cuprate materials. We further describe how subtle variations in the couplings between layers can lead to a variety of stripe ordering arrangements, and discuss the implications of our results for recent experiments in underdoped cuprates.
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