Multiple rate covers from the 1850s and 1860s are rare. Double, triple and quadruple rate covers aren't that hard to find, but covers paying 5 or more rates are rare. William K. McDaniel published a census of 1851 and 1857 issue covers with 3¢ stamps in the USPCS Sesquicentennial book and he recorded just 47 covers. The covers are not popular with collectors because they tend to be hard to display, be in poor condition, and are often courthouse covers that may have been "liberated" from government offices.

Here is an example of a 5 times rate cover from Harroldsburg, KY