Generally aero bars clamp to the bulged stem of a bar with road bar specifications. That is, 26.0mm for traditional bars or 31.8 for modern OS bars. To the best of my knowledge, aero bars are not intended to clamp to the outer (23.8) section of any bar. This may be a matter of strength or leverage as you move farther out the bar.
Companies that make a lot of aero equipment (Profile Design etc.) also make a series of bars with extended stem areas so that aero bars can be clamped on a little farther out if the rider desires that setup for comfort. Some of the cheaper OS bars that I have seen, have a stem area taper so close to the centerline that fitting aero bars is almost impossible.
When you change over to base bars instead of road bars, this problem is a little less likely as most base bars have a wider stem area.
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