This is easily done using a much simplified version of a solution I provided for Parallel execution of shell processes. Refer to that solution for an explanation of how the file locking works.
@echo off
setlocal
set "lock=%temp%\wait%random%.lock"
:: Launch one and two asynchronously, with stream 9 redirected to a lock file.
:: The lock file will remain locked until the script ends.
start "" cmd /c 9>"%lock%1" one.bat
start "" cmd /c 9>"%lock%2" two.bat
:Wait for both scripts to finish (wait until lock files are no longer locked)
1>nul 2>nul ping /n 2 ::1
for %%N in (1 2) do (
( rem
) 9>"%lock%%%N" || goto :Wait
) 2>nul
::delete the lock files
del "%lock%*"
:: Launch three and four asynchronously
start "" cmd /c three.bat
start "" cmd /c four.bat