Exemption 3585 is an exemption to 14 CFR 121 dispatch requirements for weather originally requested by Peoples Express. Lots of airlines have requested similar approval, and here is an example on regulations.gov for Air Transportation International.
The exemption that they asked and were approved for was:
...an exemption from §§ 121.613, 121.619(a), and 121.625 of Title
14, Code of Federal Regulations (14 CFR) to the extent necessary to
dispatch airplanes under instrument flight rules when conditional
language in a one-time increment of the weather forecast states
that the weather at the destination, alternate airport, or both
airports could be below the authorized weather minimums when other
time increments of the weather forecast state the weather conditions
will be at or above the authorized weather minimums.
In other words, if there is a conditional or temporary weather condition that is below minimums at the destination or the alternate airport at the flight's ETA1,2, where the flight could not normally be released, they can depart under the 3585 exemption as long as a second alternate that is above required minimums3 is filed in the flight plan and enough fuel is carried to reach the furthest alternate plus the required 45 minute reserve. There are a few other requirements too (training, manual and OpSpec revisions, etc.) but you can take a look at the letter to see them.
The exemption must be requested of and approved by the FAA for each air carrier that wants to use it.
1 The forecast weather conditions at the destination airport must not be less
than one-half of the lowest weather minimum visibility value established
for the instrument approach procedure expected to be used at the
2 The forecast weather conditions at the first alternate airport must not be less than one-half of the alternate weather minimum ceiling and visibility values
specified in ATI’s operations specifications for that airport
3 With respect to the second alternate airport listed in the flight release
pursuant to this exemption, the METAR, the appropriate time increment of
the TAF, or any combination thereof for that airport must indicate in the
main body and remarks section of the METAR or TAF that the forecast
weather conditions will be at or above the alternate airport weather
minimum ceiling and visibility values specified in ATI’s operations
specifications for that airport