Can weather groups contain multiple descriptors in a METAR?
No, a METAR descriptor can only appear once in a METAR or line of a TAF. That is because METARs and TAFs report weather phenomena in the format of 

[Intensity][Proximity][Descriptor][Precipitation][Obstructions to Visibility].


Thunderstorms, for example, are one descriptor; therefore, thunderstorms (TS) will only appear once.


Intensity

Applies only to the first type of precipitation reported. A “−” denotes light, no symbol denotes moderate, and a “+” denotes heavy.
Proximity

Applies to and reported only for weather occurring in the vicinity of the airport (between 5 and 10 miles of the point(s) of observation). It is denoted by the letters “VC.” (Intensity and “VC” will not appear together in the weather group.)
Descriptor  

These eight descriptors apply to the precipitation or obstructions to visibility: 

TS = Thunderstorm
DR = Low drifting
SH = Showers
MI = Shallow
FZ = Freezing
BC = Patches
BL = Blowing
PR = Partial

Precipitation

There are nine types of precipitation in the METAR code

RA = Rain
DZ = Drizzle
SN = Snow
GR = Hail (1/4" or greater)
GS = Small hail
PL = Ice pellets
SG = Snow grains
IC = Ice crystals
UP = Unknown precipitation

Obstructions to Visibility
There are eight types of obscuration phenomena in the METAR code

FG = Fog
HZ = Haze
FU = Smoke
PY = Spray
BR = Mist
SA = Sand
DU = Dust
VA = Volcanic ash