Yanking and cutting text overwrites the previous contents of the register by default. But for named registers, there is a way to append yanked/cut text to the the clipboard instead. The trick is using the upper-case version of the register name:

"ayy // Yanks current line to the named register `a`
"Ayy // Yanks and appends current line to the named register `a`.
"Ayap // so on and so forth...

For more info on Vim registers: :help registers