When a relevant variable unnamed on either axis changes, can the curve NOT shift? Source: pp 40-41, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw


  her demand curve would shift to the left (to curve D3).
  In economics, it is important to distinguish between movements along a curve
  and shifts of a curve. ...
  ♦ There is a simple way to tell when it is necessary to shift a curve: When a relevant
  variable that is not named on either axis changes, the curve shifts. ♦ ...


Is the last sentence of the excerpt (within $\mathbb{R^2}$) above really true ? (I surrounded it with lozenges ♦) 

What if ceterus paribus, a fixed number $&gt; 1$, of relevant variables changes? Can they counteract each other, or even equilibrize all the changes so that the curve stands unmoved?
The scenario of counteracting changes in relevant variables is theoretically possible, but unlikely in practice.

As an example that might come fairly close, consider the supply curve of oil in a small developing country which imports all its oil and subsidizes its sale, the subsidy being at a flat rate per unit.  The country will be a price taker for oil, so its domestic supply curve will be horizontal at the world price less the subsidy.  Now suppose the world price falls, and the government takes the opportunity to reduce the subsidy by a similar amount.  Either change on its own would shift the supply curve (the former down, the latter up), but together they could largely counteract each other.  Even in this case, however, it is implausible that the supply curve would never shift at all.  For one thing, the world price of oil is constantly changing, and it would be impracticable to adjust the subsidy so frequently.  For another, there would inevitably be time-lags in adjustments.

So although you correctly identify a theoretical exception to the statement by Mankiw, it is unlikely to be of much practical significance.