The Summoning Engine was apparently a device originally designed and built by Lucrezia Mongfish but re-built by Lady Vrin after Loremistress Milvistle destroyed the original. It was used to imprint a copy of Lucrezia's consciousness and personality on to the mind of another. It was kept in its own chapel in Sturmhalten Castle until Lucrezia, anticipating Klaus's interference, had her Geisterdamen move it to parts unknown.
Prince Aaronev Wilhelm Sturmvoraus apparently assisted the Geisterdamen in collecting young girls and women as test subjects for the machine, in hopes that one of them would turn out to be a suitable host for Lucrezia. All of these victims seem to have been killed or .
At one point, Lucrezia, while in the body of Agatha that there were errors in the reconstruction of the device by Wilhelm and the Geisterdamen, which might explain why it didn't work on subjects other than Agatha. Once Lucrezia was present, however, she was able to improve the device to the extent that it was able to download a copy of Lucrezia into an advanced Clank brain.
One thing that was not expected was that Agatha's original personality would be able to fight back against the superimposed Lucrezia personality. This may be due to imperfections in the device's reconstruction, or Agatha's inherent strength of mind, but no one can say for certain.
The device does not appear to grant the possessor any memories of the possessed victim; while Agatha was possessed, the superimposed personality showed no hint of expecting to have access to her memories (and several times asked questions about, or displayed ignorance of, things Agatha would obviously know, without any hint of irritation or confusion at having to do this), implying that this lack is part of their usual function and not due to imperfections in the device's reconstruction.
Lucrezia has her own theories of Agatha's resistance, and the revelation she can take information from the Lucrezia personality. However, her mother's persona seems to influence her emotionally .
The Geisterdamenwith them when they left Sturmhalten.
Later, Lucrezia refers to it as aand refers to her numerous copies as callings. At the same time, it is stated that she expanded the parameters of the device, potentially meaning there are more Lucrezias around now.
The copies have a mutual registry code that involves blinking and other facial tics to identify themselves, as observed by Tarvek.
Lucrezia's Secret Lab
Lucrezia's secret laboratory in Castle Heterodyne has a simplified Summoning Engine that she uses to attempt copying her consciousness to Zola. Lucrezia's comments suggest that the Engines have two functions - the Beacon, which summons Lucrezia's essentia, and mind transfer.
The Shining Brotherhood used a modified Summoning Engine, source unknown, as part of their Summoning Ceremony.