Pathfinder Question; The Runesage (from Adventurers Guide)

arcane focus – could a wizard somehow have already prepped objects (like backup wands, staves, or whatever object) as backup arcane focuses? for instance, say you’re a runesage (the class I’m looking at), and it tells you to treat your floating rock similar to an arcane focus when switching the school it channels (i.e. inscribing a new rune into it). what if~ prep 4 extra shiny gems with the other schools runes on each one, having paid the costs already to have made them. and simply switch out which rune (school) you prep with each morning. ?