That option seems to only be available to the windows ftp client. For a similar result, you can install an ftp client that you can script. NcFTP is pretty friendly to this. Wget would work too.
With ncftp, you'd have a file with your "get" list and one with your login credentials if you don't want to enter them every time. (Be aware of the security risks involved)
From the command line using bash you'd either enter the following into a script or just run:
while read line
ncftpget -f <FILEWITHCREDENTIALS> $line -bb
done < <FILEWITHLIST>
Your credentials file will be in the form of
-bb submits each file as a batch job waiting to run. Calling ncftpbatch will run the job. Doing this should limit it to one connection.
Other options would be -b (just kick the job off in the background immediately) and dropping the ncftpbatch call, and using the user/host/password options in the command instead of -f.
You can find ncftp here and here if it's not already installed.
For wget you can use a similar looping script and replace the ncftpget call with
again, if it's not already installed, you can get wget here or for with either program look up the appropriate package manager for your version of Solaris.
You can find more information about the programs with the man pages or through a quick web search.