Can I encrypt data with multiple keys and decrypt with one?
Here is a candidate system, based on an ordinary message cipher $\mathcal E_\kappa(p)$ and $\mathcal D_\kappa(c)$ so that $\mathcal D_\kappa(\mathcal E_\kappa(p)) = p$ and $\mathcal E_\kappa(p)$ is indistinguishable from uniform random noise to anyone who doesn't know $\kappa$.

Let $k_i$ be the $i^\mathit{th}$ encryption key, let ${E^i}_{k_i}(x)$ be the $i^\mathit{th}$ encryption function, let $k$ be the decryption key, and let $D_k(x)$ be the decryption function.  We want to define $E^i$ and $D$ so that $$D_k({E^{n-1}}_{k_{n-1}}(\cdots({E^1}_{k_1}({E^0}_{k_0}(x)))\cdots) = x,$$ but otherwise we want all the intermediate ciphertexts, ${E^i}_{k_i}(\cdots({E^0}_{k_0}(x))\cdots)$, to be indistinguishable from uniform random noise to an adversary who does not know $k$ or the $k_i$.

To this end, define

\begin{align*}
  {E^0}_{k_0}(x) &amp;= \mathcal E_{k_0}(x), \\
  {E^i}_{k_i}(x) &amp;= x, &amp;&amp;\text{for $i &gt; 0$.}
\end{align*}

Decryption is easy: the decryption key is simply $k_0$, and $D_k(x) = \mathcal D_k(x)$.



If this doesn't satisfy your needs, you will need to be more specific about what your needs are so that they meaningfully exclude this system.  ‘Meaningfully exclude’ implies that you have to give some reason related to your application why this won't work, rather than just say you don't like it and the $E^i$ functions have to actually do something.

In particular, it will be helpful for you to identify who changes the key and why.  Are you the sender and recipient, and are you changing your password because it got compromised and surgically removing all traces of the previous key derived from it and ciphertexts encrypted with it from all storage systems everywhere?  Are there multiple parties involved, like members of an organization who have split administrative functions to avoid unilateral power to doctor records?  What are you or they all trying to accomplish?  What is the adversary you hypothesize able to do to manipulate the resources they are trying to accomplish it with?  What do you want to make sure the adversary can't do?