Parallel Movement

Sliding. The ability to look at or move between spiritron worlds. Archimedes, being the system administrator of SE.RA.PH, can navigate these worlds with precision.
In short, it is the power to travel between parallel universes.
Ordinarily, looking into another world is the most one could manage with this ability. To send one’s consciousness there, let alone one’s “physical” presence, would be impossible, even in SE.RA.PH.
The most one could theoretically do is send a record, and even then, the Cyber Frame would not be able to withstand moving against the flow of time or the walls that separate each world, and it would be disintegrated.
The only reason why Archimedes and Corroded Elizabeth are able to move between worlds unharmed is because they have been corrupted by the Umbral Star. The Umbral Star’s spiritron cells, which run through their bodies, strengthen their very existence.
During the incidents of EXTELLA, the Moon Cell recorded the existence of Archimedes and Corroded Elizabeth, stifling their ability to slide between worlds in the future.
For Archimedes, the best opportunity to further his agenda was during the time period before he is discovered to be a vassal of the Umbral Star. His plan, of course, ended in failure.
By the way, if Archimedes or Corroded Elizabeth had slid to another world, the “self” that was already in the target world would be ejected to a similar world, and then combined with their existence in that world. (How complicated…)
If there was no world similar enough to meet that criteria, they would be assimilated into the strongest “self” currently in existence.

Translator's Notes
  1. ^ Also translated as “Adjacent Movement,” “Parallel World Travel” (Fate/EXTELLA) and “Sliding.”
Fate/EXTELLA material: Encyclopedia of Fate EXTELLA