rothnd wrote:
...I would like to remove ToshibaTM without affecting ToshibaStorage's data if at all possible. And then setup a new TM partition on the Lacie without affecting its original data. Is this possible?
Ok, a bit of background may help. Your LaCie drive is currently formatted with HFS+; whereas, your Toshiba is formatted with APFS. The big difference is what used to be called "partitions" in HFS+ is now called "containers." But there is one significant additional difference: APFS containers are dynamic. Also, you can easily create multiple volumes within an APFS container.
That means, it is far easier, when you have existing data on a drive, to add container, than partitions. The latter being "fixed" in size.
In your case, ToshibaTM is an APFS volume inside the disk11 container. You can simply erase it using the Disk Utility if you no longer want it. This will not affect ToshibaStorage.
However, for your LaCie, you would first have to create a new partition from the existing one. The key is how much data is currently taking up storage space in the existing partition. You would want the new TM partition to have 2-3x the storage capacity of the Macs that you are backing up with Time Machine (of course, I'm assuming that the TM label is what this is meant for.) If the LaCie does not have adequate space left, this will not work.
Let us know how you would like to proceed. Also, if you don't mind, please take a screen shot of ToshibaStorage. Based on what you have provided, it appears to be a second APFS container on Drive Dock 1.