[alicp (OP)]

Could there ever be a group of days or weeks when one storm follows another to create unknown amounts of devastation? Could a tsunami happen alongside an earthquake, a hurricane, a cyclone, a blizzard, an ice storm... etc? Would love to know a professional's opinion?

Thank you,
Alicia

[Bill.D.Katt.]

Tsunamis quite often happen in relation to earthquakes. I think a cyclone is usually in the Southern Hemisphere and a hurricane is in the northern (someone please correct me on this if I'm wrong). Since hurricanes and cyclones are tropical in origin, I doubt that a blizzard could follow, but there could be a very large cold front moving down at the same time, possibilities are almost limitless. If you are considering these storms not striking the same place, then I would say yes, it is very possible; but I'm not a professional.

[CliffordK]

Well...
I would vote for a Blizzard at -91°C (-132°F)  in Vostok.
But, I suppose if one is living down there, one would expect cold weather.   [xx(]

Following that...
You might try a day at 57.8 °C (136 °F) in Al 'Aziziyah, Libya (that was 1922..  NO AC [!])

Hurricane Season can stretch into December.

There is no reason why a city couldn't get pummelled with heavy arctic snow.
Then have a hurricane move up from the South a few days later.  A warm rain in a heavy mountain snowpack could cause secondary flooding (beyond what the Hurricane causes).

Heavy Subsidence after an earthquake...  and a secondary storm might be irrelevant. 

When they talk about hail in Nebraska.....
7" Hailstones  []
http://www.noaanews.noaa.gov/stories/s2008.htm


Oops, that's old news... 8" in South Dakota.
http://www.newsnet5.com/dpp/weather/weather_news/Big-hail-Largest-hailstone-ever-found-in-South-Dakota-this-week


You might add a larger asteroid to the list.  An asteroid impact of a 1km asteroid could wipe out any city in the world...

Volcanoes...  locally devastating, but can have global effects including global cooling.

[Kryptid]

If the hypothesis in regard to 'hypercanes' is valid, then such a storm could be quite devastating as well. An asteroid impact superheats ocean water which triggers the formation of particularly intense hurricanes (with winds in the range of 500 miles per hour).

[nicephotog]

Nuclear Winter.