I am trying to copy multilple files and the syntax is source + source + source destination. However, only the first file is being copied to the destination. They are all files and not directories. I do not want to use XCOPY. Thanks for any help!

Assuming your files are in one directory:

copy [source] *.* [destination] or copy [source] . [destination]

example: copy c:\oldfiles\. c:\newfiles

COPY used from the command prompt is not a windows command, it is a DOS command.
Using the + isn't what you think. What that does is envoke the append pipe which places the path to the files as the first entry following the current directory in the path statement.
Copy from the command prompt can only work with multiple files if they are part of a group that can be found using a wildcard, like *.txt will select all files with the .txt extension.

copy c:\files\importdoc.txt f:\backups
copy c:\files\importdoc1.txt f:\backups
copy c:\files\importdoc2.txt f:\backups
copy c:\files\importdoc3.txt f:\backups
copy c:\files\importdoc4.txt f:\backups

XCOPY is just a newer version of the old copy command. It includes all the same switches with more functionality. Odds are, you'll need a copy command for each file. You could do a switch directory to the location of the files if most of them are in the same place. aka
cd C:\files\
copy import.doc to f:\backups
<leave a few files>
copy otherstuff.jpg f:\backups