Finally had time to do some more reading, and the story remains chaotic. I’m currently about halfway through chapter 5 of 10.

The Catian professor who won the fight on the space station (“old age and treachery beats youth and skill…”) arrived and promptly snuck out of the ship to explore Earth on his own. Given his extreme age, at first they were concerned that he might get himself into trouble; then they searched his room and discovered that his studies of Earth had focused on “theory and practice of crime”, and got worried. He didn’t smuggle any weapons, but his old-fashioned assistoroid Igor is quite capable. Igor also sabotaged the transporters, so they don’t know exactly where he went, but it could only be one of three locked-in destinations: Kio’s neighborhood, Shinjuku, or Nakano Broadway. The gang starts searching, deciding not to bring Antonia’s forces into it for now; Kio and Aoi head to Nakano, Manami to Shinjuku (planning to link up with Director Kawasaki), taking advantage of Eris’ new “Mini Ruros” flying car to get there quickly.

Meanwhile, Antonia has decided to play hooky and sneaks out on her own, accompanied only by her assistoroid Heihon. A frantic Sara chases after her.

Informed by her bosses that something’s up, goth-loli MI6 agent Black Amarylis (who turns out to be a bit of a cyborg) does some preliminary snooping around Kio’s house, then decides to explore the neighborhood. Another team of agents manages to get the drop on her, planning to brainwash her into serving as a double agent, when their kidnapping attempt is interrupted by the strum of a guitar and the theatrical arrival of a mysterious figure in silvery robes and a ten-gallon hat, with a cloaked, child-sized companion. Guess who?

Taking advantage of the distraction, she takes out the two nearest enemies in one shot, then tackles the Catian professor to get him out of the sniper’s line of fire, whose subsequent shots are intercepted by the assistoroid. The three of them run off together, and she’s quite surprised when she gets a good look at her no-longer-disguised rescuers.

Notes:

• The Professor, Arkamatsu, is truly ancient by Catian standards, at 570 years. In passing, it's mentioned that few live more than half as long, and many of those have lost interest in life; this is considered one of the biggest problems in Catian society.
• He has experience both in space exploration and one-shot-kill hand-to-hand combat, and both Chaika and Kuune studied under him in their youth. Kuune in particular has mixed feelings about him; he is of course a dirty old man with a fondleness for large breasts.
• Nice use of the suffering passive when Kuune informs Kio: "Kyouju ni nigerareta" ("we've been escaped by Professor").
• Black Amarylis (which is not the goofiest codename he comes up with in this book...) appears to be about 12, but it's mentioned that she's looked that way for several years, and is actually 15-16. Presumably something to do with her cyborg parts.
• In her first scene, she announced herself by her real name, Alicia Maria Yorkshire, and the terrorists she was confronting immediately knew her codename. Given that people used to do the same thing with Aoi, one wonders why these agencies bother giving them codenames in the first place.
• She'll apparently be a regular, given that she's on the cover of book 12. It's only hinted at here, but it looks like she's Sara's long-lost niece. I guess a weakness for assistoroids runs in the family.