I don't use ASBU, so cannot comment. I use my own proprietary method in CS, described in another thread here, and for it I sharpen the native size file optimally before up-sizing, then re-sharpen that file as needed via an indirect fractal method, also described in the article.
The basics are:
1) Get your file the way you want it looking AT ITS NATIVE SIZE, INCLUDING OPTIMAL DETAIL ENHANCEMENT AT THAT SIZE, but make sure it is NOT over-sharpened. Much better to be not sharpened enough than too much.
2) Uprez to your desired output size plus 15 - 20% in one shot using Bicubic Smoother. Example: If you want your final print to be a 16x24 at 360 PPI, then upsize it to 16x24 at 420 - 440 PPI. Note that final print resolution setting should be optimized for the printer/media combos being used.
3) Once at the over size, you can add some targeted edge sharpening if desired. Usually not required or recommended until one goes larger than 16x24 from a typical 8-16 MP file.
4) Downsize to target size using Bicubic Sharper. Example, take our above image from 16x24 at 440 PPI down to 16x24 at 360 PPI. (This is an indirect, fractal sharpening step in itself, automatically targeting final print size.)
5) Add any required edits specific to the output size.
6) Print it.
The above steps will generate a very nice large print file, though admittedly I have a few additional "secret sauce" edits I keep to share with the workshop attendees.