Okay, so I am creating a multi-boot live cd with various linux distributions including Debian and Mint. Each distribution will be used to focus on diagnosing and/ o repairing a specific issue best suited to the specific distribution. However, there will be no persistent storage enabled on this drive following the installation of the ISOs. As a result, I will need to install the necessary software to each distribution's ISO prior to writing the images to the flash drive with YUMI.

Is there a way to do this? All methods must be compatible with windows because that is the primary operating platform that I am limited to at this moment. I am not interested in tools that work to create custom live CDs for Ubuntu linux distributions as I will not be using any Ubuntu ISOs and I am not willing to compromise in this respect.

There was software created specifically for this purpose called remastersys. There was one version specifically for Debian and another for Ubuntu and since Mint underneath is Ubuntu, it also worked with Mint. Since the developer was one individual and it was a tremendous amount of work to maintain it and he got little help and a lot of demands, he quit. I doubt if it would work on new releases of Debian or Mint. The last Mint it worked on for me was Mint 13.

You might try an online search for modifying Debian/Mint iso which is going to be much more complicated.

I'm not sure what you mean by 'compatible with windows'.

The Knoppix web pages had all of that if you want to do it by hand.

The only way I know of doing this from windows is to install qemu to run a linux distro or some other free virtual machine. Several issues require you to use linux.

The only other way I know of is to use SuseStudio.com and build your custom version which won't be exactly a live type.

I figured that using a virtual machine would be one of the ways that I could do it. My only question would be, how would I create a copy of the modified ISO?

If you don't or can't use some app like above then the steps for modifying a cd is something like this.

General steps.

Install VM.

Take common distro generally or one that has tools easily or you like and install it to vm.

Use an app to expand the data off the cd. Most live cd's are compressed. There are a few other folders and files that you may or may not need but get that compressed filesystem off.
That data needs to be in it's own working folder and you do it from linux. So you'd have a booted linux vm that is your construction computer(virtual computer).

Then you either have to make that system bootable to add in changes or depending on the app you want you can add it to you build area.

Once it is complete you re-compress the data using hopefully the same version level of compression and see if it fits back on your target. Something like mkiso or some command like like that. You get the entire iso package at the start and this all comes with that package.

Now if it doesn't fit for some reason you may be able to change compression level. Go to a dvd image, or remove stuff you don't need.