A recently introduced construction principle is investigated with the objective of designing stable multiply negative quasilinear ions. The discussion is exemplified for chainlike potassium fluorides for which explicit calculations are carried out. The stability of the newly designed chains to fragmentation and to electron autodetachment is studied and found to depend on the terminal groups of the chains. The shortest chain which can hold three excess electrons contains five fluorine atoms; the one which can stabilize seven excess electrons has 19 fluorine atoms.