There are a few different triplizers. I believe the Willow Triplizers mount like a normal ring, and rotate the bolts for the inner ring to between the arms.
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Shimano used a triplizer on some of their cranksets. The 6703 rings are still available, and a triplizer of sorts, but with the inner bolts inline with the outer bolts. In this case, the shelf for mounting the ring has to be ground down flat.
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In both cases, a spacer is used to set the spacing between the inner and outer rings so teeth aren't mashing in the wrong spot.
Your 39 to mid 40's ring is mounted as an inner ring, and the triplizer is mounted inside of that.
The outer ring is either mounted as-is, or replaced with a bashguard (or with teeth ground off as per @
Bianchigirll.
People have also successfully converted some of the vintage flat spider cranks such as the Campagnolo Strada/Nuovo Record cranks by simply drilling the spiders and adding spacers.
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I have thought this modification might also work with first generation Dura Ace cranksets.