Our situation is as follows:
The desktop HDD is not big enough for the projected use of LR, which is the range of 20k images per year. We'd like to have one extensively keyworded catalog linked to three external hard drives. Is this possible?
Yes it is Possible
Recommend you to have your Catalog setup on SSD Drives with Fast Read/Write speeds.
If you already have Pictures on your Internal drive and want to move them over,This video might be helpful How to Copy Files to an External Hard Drive in Lightroom | The Complete Picture with Julieanne Kost | Adobe TV .
Let us know if that helps