You’ve got some options, jump to the end for the summary.
So let’s break this one down…

Copyright (c) 2012 [Acme Corp]

This is the Copyright notice and it belongs to Acme Corp. It was claimed in 2012, which is relevant because Copyright does eventually expire.

If the claim was actually given to “Acme Corp”, ie. it was boilerplate cut & pasted from the MIT example, then you could almost claim that there is NO copyright on this work. Acme Corp is a fictitious organization, and failing to update the boilerplate puts the claim on dubious grounds.

But let’s be good citizens, and grant the copyright to the actual claimants.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the “Software”), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

This next section, the Permission notice, is stating that you can do just about anything you want with the code, including modifying the licensing agreement! The catch is that you can’t change the license on the existing code – you can change only what you modify.

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

This part simply means you have to persist the notices that are above.

So, what can you do?

• You can and should lay copyright claim to the code you wrote and / or modified.
  • To do so with the same MIT license: Just add your copyright notice after the 2012 Acme Corp copyright notice in the files you modified.
• You can license your modifications under a different license, if you so choose.
  • To use a different license: Add your copyright and license notice after the entire 2012 Acme Corp block (copyright, permission / license, exclusion of warranty) in the files you modified.

In the simplified case of your question, here’s what you need to do:
Emphasis added to highlight the differences.

Original work Copyright (c) 2012 [Acme Corp]  
Modified work Copyright 2012 Steve Bennett  

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

I am not a lawyer. The following is assuming US copyright law, and is specific to the MIT license.

The person that wrote the library owns the copyright on the code that he wrote. Only he is allowed to specify the license for that code. Per the license terms you must keep the copy of the LICENCE.md file, verbatim, with the code that he provided you.

You own the copyright to any changes or additions you made to the code. You’ve created derivative code. Only you are allowed to specify the license for your changed or new code. If you are creating a separate fork of the project, you must select a new, separate, license for your project. You must still keep the old license since it applies to the unmodified code.

If you wish to push your changes back to the original project, you still own the copyright to your changes. You must provide the original author with a license that allows him to redistribute your changes as part of his project, under the license that he chose.

More formal projects would ask you to sign a contributor license agreement or copyright assignment, but if it’s an individual he probably wouldn’t even realize that he needs one. This is usually done so that he may integrate your code into his codeline without changing any of the existing license terms. Typically a project will include an AUTHORS file listing all of the project contributors, but this is not mandated by the MIT license.

I wouldn’t worry too much about the copyright bit. I believe in most cases copyright applies automatically whether you claim it or not so the (c) 2012 blah headers are mostly noise. That being said you don’t want to mislead people so as you’re including the license you should indicate that by saying the software was originally licensed as… or that parts of the software are licensed as…

As the source is already publicly available it should already be clear who the author(s) are, and, as it seems that no money is changing hands, it would be pretty hard to make a claim for damages even in the event that the authorship is contested.

Perhaps a more pressing is issue is that of being a good web citizen. People that provide open source software are doing the community a service, and we should strive to make that a positive experience for all. So my advice is to ask your question directly to [Acme Corp] and try to establish a relationship with them whereby you both benefit.

You should not change the copyright.

You are technically entitled to what remains of a copyright (after being “filtered” through the license) to whatever you added/changed. As long as there is a clear, unambiguous record of your changes (github), you can add a copyright notice under your name in the modifications section if you wish, though this is generally not done.

You could/should add a comment (or to an existing one) indicating who made the changes and when (if they aren’t doing this already, don’t start it).

/*
    Copyright (c) 2012 Frob Co.

    Permission is hereby granted, free of charge, to any person obtaining
    a copy of this software and associated documentation files (the "Software"),
    to deal in the Software without restriction, including without limitation
    the rights to use, copy, modify, merge, publish, distribute, sublicense,
    and/or sell copies of the Software, and to permit persons to whom the Software
    is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included in
    all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
    OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
    IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
    CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
    TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE
    OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
/*
    Changes
    1-1-2012: YOU: Made a frob
*/

I believe this is the correct way to paste the MIT license into a file, though I’m not a legal expert (I’ve never seen it without the “yelling” part of the notice).

So far, I’ve handled this by adding contributors to the list of copyright holders, and leaving the licence text unchanged.

Essentially, this means that you are publishing the additional changes under the same licence as the others did before, and that the derived work should be licenced under these terms as a whole. This also means that the original authors may no longer re-licence it, as they are no longer the sole copyright holders (they can re-licence their original work without your additions, obviously).

As a non-lawyer, my interpretation of the last sentence is that you are not allowed to remove copyright notices, but you can add your own.