Couldn't Modify Partition Map using external disk
I found my silly error. The solution: in Disk Utility, I chose specifically the partition that wasn't able to increase in size, then I ran the verification. It turned up problems so I ran the repair command. Then I was able to increase the size of the partition. Mt external hard disk, Mac Swap, is now only one partition. 

To be clear about my error, in case you're reading this for help. In Disk Utility, there is always both an icon for the disk as a whole and below it immediately there will be all of its partitions. If you run the verification on the hard disk as a whole, then it may not catch what's wrong on your partition.