Vita:PSVSD (11XX)

Since the modem/GPS card on the PCH-11xx series uses a standard miniPCIExpress connector (USB/SIMcard pins only), albeit with a non-standard ¾ length card, it can be replaced with another USB-based device. While the official firmware is rigged to only support USB mass storage for PSTV recovery, that's nothing a 3rd party plugin can't fix, right?

The PSVSD, invented by Yifan Lu in August 2017, is an ordinary microSD to USB card reader designed for this form factor. It can optionally be combined with a flat cable microSD extension (or even a reverse SD to microSD adapter) to allow external access to the card via the SIM slot.

Other mass storage devices are also viable...

On the Vita 1000

The non-3G OLED system lacks a miniPCIExpress connector and a few discrete inductive filters (replaceable with a short) completing the power and data lines, however it is inconclusive whether this is sufficient to restore USB support.

Software

VitaShell

VitaShell offers an USB storage mounting feature in its main menu, originally invented for PSTV users and in fact pre-dating the PSVSD concept.

usbmc

The original plugin by Yifan Lu.

https://github.com/yifanlu/usbmc/releases

StorageMgr (Recommended)

A newer plugin by CelesteBlue, allowing to assign a mountpoint to any supported device (SD2Vita, USB storage, memory card, internal virtual memory card partition).

StorageMgr is the recommended solution to use with a psvsd.

YAMT

Yet Another Mount Tool is the newest plugin that allows for management of the PS Vita's storage partitions. It also supports the SD2Vita and psvsd, although it has poor functionality with the psvsd so it is recommended to use StorageMgr with it instead..