Depends on a few things... hitch height, king pin setting, how far the nose hangs over the king pin (if any), and of course the height of the crossover box itself.
I have a low profile box, and have no issues at all.
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Tom
2013 VOLTAGE 3200 (EPIC I & II)
2014 Ford F-450 PLATINUM
2018 BMW R1200GS RALLYE
This is the tool box I have on an F350 that i use to tow a Gooseneck Horse Trailer and a Fifth Wheel Travel Trailer with, wanted a low profile box in case I needed to Jackknife in tight areas, the box has a slide cover that works out very well, it is only 2 1/2" in heights
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19 F450 Crew Cab 4x4 Lariat, 17 Voltage 3970 Epic 200 Watt Renogy Solar System
I have 8ft bed fords, we use cross bed boxes that stay below the rails, so we can still use the toneau covers, and they do not interfere with towing fifth wheels trailers.
It's your rig, do what you want, I've towed a 5th wheel with a cross over tool box for 41 years and no problems, just set up your hitch according to the clearance you want from trailer to the tool box....