Q:

How to create a new partition for OS X, then remove the original one

I want to clean install a new version of OS X, so I was thinking to create a separate partition, transfer all applications and settings from my old system and then remove the old partition and make a new one the only one.
But when I created a separate partition for El Capitan, I realized it is not possible to resize it or remove the original one. Here is a message I get from Disk Utility:
"You can only merge this partition with the one before it. To do it, click -"
When I click "-", all data will be erased and free space merged into the first partition. 
What is the best way to do a transition in my situation? Is it possible to create a new partition "before" the original one?
Here is the info from Disk Utility:

And from the Terminal:
/dev/disk0
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *500.3 GB   disk0
   1:                        EFI EFI                     209.7 MB   disk0s1
   2:          Apple_CoreStorage                         427.1 GB   disk0s2
   3:                 Apple_Boot Recovery HD             650.0 MB   disk0s5
   4:                  Apple_HFS El Capitan              72.2 GB    disk0s4
/dev/disk1
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:                  Apple_HFS Macintosh HD           *426.8 GB   disk1
                                 Logical Volume on disk0s2
                                 991EF790-B05D-45BB-B326-6CDC7D75A172
                                 Unencrypted

A:

With Apple's OS X tools you can't expand the start sector of a partition to lower sector numbers. You have to choose another method.
You may accomplish your objective if less then one half of the net capacity of your hard drive ((~disk size - size of Recovery HD - size of EFI)/2) or less then one half of the main volume is occupied. If you miss the threshold narrowly you may remove swap files, sleepimage and clean the temp folders to lose further GBs.
In this particular case you may add a second volume with the same size as your then narrowed previous main volume, which is equivalent to splitting the available space in two equal volumes (with the first volume still containing your old OS X installation).
After installing your new OS X to the new volume ("El Capitan") you may transfer your apps, settings and data to the new volume.
After migrating your stuff you have to delete the old CoreStorage Logical Volume Group (the superior Macintosh HD) with:
diskutil cs delete lvgUUID

with lvgUUID: UUID of the Logical Volume Group. To get the lvgUUID use:
diskutil cs list

Deleting the Logical Volume Group will automatically create one new classical JHFS+ volume with the name "Untitled" occupying all available space on the disk. 
Now clone your new volume "El Capitan" to the empty volume "Untitled" with an appropriate tool (Disk Utility/Carbon Copy CLoner). The former "Untitled" will be renamed to "El Capitan". So rename the former "El Capitan" to "El Capitan_Old"
After successfully booting from "El Capitan", delete "El Capitan_Old" with Disk Utility and expand "El Capitan" to the full available size of your disk.

If more than one half of your (old) main volume is occupied you need an external disk to migrate or you have to delete some data.

