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I see that Nicholas Wolff once won a game of Bishop Knight Morph Factor. Joe Joyce's Pieces thread from 2009 contains some interesting comments on various pieces, including Changelings. Looking back on my 2007 comment here, what if a Pawn promoting to a Rotator can choose the R/N/B mode? That allows a player promoting to a Rotator [N mode] to deliver a needed Knight check, while obtaining a new piece that is (perhaps) twice as valuable as a Knight.
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David - thanks for suppling information regarding pieces that change. Unlike the obvious Pawn promotions in Chess, more limited pawn promotions in Xianqi, or piece promotions in Shogi, my first piece that could transform was the Morph in Pillars of Medusa. It started out moving as a Bishop, but it could optionally change into a [Morph of] the piece or Pawn it captured (on the turn of capture). Several years ago I bought a Steve Jackson game called 'Proteus' - It is played on a standard 8x8 chess board. The pieces are 8 identical cubes per player, with a different piece on each of the 6 surfaces. The pieces can rotate up or down to increase or decrease their value. I'll not spill out the rules here, but will mention that it is one of my all time favorite variants.
In 2001 David Howe posted Chess on a Longer Board with a few Pieces Added. His Changeling piece starts out as a Halfling Bishop and alternates its movement with a Halfling Rook. A Game Courier search for [Chess on a*] will turn up old games in this variant, plus some others.
I once considered replacing the Queens in standard chess with Rotators, moving R-N-B-R-N-B and so forth. WHITE: King b3, Rotator[Rook mode] g2, BLACK: King b1.
White to move and mate in three moves
1. Ra2=N Ka1 2.Nc3=B check Kb1 3.Be1=R mate.
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I see no reason why an RNB Rotator would be worth more than a Rook. I would expect it to be worth significantly less than a Rook even in R mode. (The current mode would fine-tune the value just like current mobility would for normal pieces.) About half-way between a minor and a Rook. I am not even sure whether it is a major piece (i.e. can force checkmate on a bare King from almost any position).