CMW can only work with one Current Item, and it can also only work with what WordPress has determined are the Current Items [in the menu in question].
For example, let’s say you have a [very simple!] menu of…
[Page] Alpha
– [Page] Omega
[Page] Beta
– [Page] Omega
[Page] Gamma
– [Page] Omega
…and you use WordPress’s own Navigation Menu widget to show that menu.
If you show Omega at the front end, then all 3 ‘Omega’ menu items will be marked (by WordPress) as “current”, with each parent item also being marked accordingly.
If you were to add a CMW instance, looking for Current Item, then CMW would find multiple current items and would elect to use the 1st one (or the last one if you set the Fallback option) as being its Current Item.
This is because WordPress looks at the here-and-now, as in “Does the page [URL] currently on display match any of the items in this menu?”. It does not reference how you actually got to the page in question, so the fact that you were previously on a “Beta” page when you clicked through to Omega is not relevant (to WordPress, although it obviously is to you!).
The only way I could achieve what your after is to not use the Page menu items, but to use Custom Links in the menu.
Eg. the above menu becomes more like…
[Page] Alpha
– [Custom Link] ../Omega/?parent=alpha
[Page] Beta
– [Custom Link] ../Omega/?parent=beta
[Page] Gamma
– [Custom Link] ../Omega/?parent=gamma
Testing with WordPress’s Navigation Menu widget indicated that clicking on the “?parent=beta” menu item navigated to the Omega page, and the only widget item marked as current was the “?parent=beta” item.
Then adding a CMW instance that looked for Current Item would correctly show me just the “Beta” part of the menu.
I’m sure there are other, programmatic, ways to achieve this that don’t result in different URL query strings, but they would involve hooking into a WordPress filter/action somewhere and (hopefully) somehow modifying its determination of Current Item.