Figured it out!
If you use a batch file with a for loop and a START command you can run sessions in parallel. For example the code below starts one (parallel) job for every file found in the working directory. Have had it up and running in production x1 week and it's working well.
CD d:\ftp\work88
for /f %%a IN ('dir /b *.zip') do (START winscp.exe /console /command "open Client44" "cd To_Be_Scored" "put -nopreservetime -nopermissions %%a" exit)