The Clip+ (and all of the Sansa line of mp3 players) has a micro SD card slot so no, full-sized memory cards will not work. The largest available micro SD card right now is 64GB SDXC. The XC (exFAT) format is not read or supported on the Clip+, but some have had success in re-formatting them to the HC (FAT32) format for use with the Clips and others.
Note though that all this extra memory will hold a lot of tracks, especially if they are .mp3 format. The Clip+ has an (official) 8,000 track database limit, although most people seem to hit this around 5,000. So unless you use FLAC or other larger sized files, it’s very likely you will not be able to fully realize the benefit the extra storage capacity gives you.
There is an alternative, 3rd-party firmware called Rockbox you can check out though. Just about everyone I know of using these ‘hacked’ 64GB cards are using it as it has no such limitation, plus the many other benefits/features it offers.