I have a 11-28 10 speed cassette on my bike now, 46-36 chainrings, slx shadow 9 speed medium rear deraileur. Is it possible to switch to a 11-36 cassette?

Yes you can switch, if it will work is another matter.

1st issue, is you are using a 9 speed rear dérailleur with a 10 speed setup, as that's shimano, that means is should have a Dyna-Sys RD as you are using MTB parts, so you really need a Dyna-Sys rear mech. Ideally what you want is something like a M675 SGS rear dérailleur for this type of setup.

Using a GS RD on anything over a 32T cassette can be temperamental even though it is spec'd to work up to a 34T, and will have some give to go to a 36T.

What type of bike are you running this on, as it sounds more like a CX setup than a MTB which a 11-36T would be associated with. You haven't mentioned the shifters you are using, which could complicate everything depending what you are using, as Dyna-Sys RD's only work with Dyna-Sys shifters.

Cx bike. Using ultergra st-6600 brifters. Wanted to use a longer cage rear so I went 9 speed mtb with the 10 shifters.

In that case, would look at s SGS 9 speed RD, a Deore (non-Dyna-Sys) should work fine.

Got to ask, what are you looking at climbing that you can't with the 11-28? I got a CX bike this year, and unless it's been too muddy for traction, have got up everything with a 11-28T that I MTB with a 11-34T without feeling the need to go any bigger on the CX at the back

More curious than anything else. Good deal on CL for the cassette. I have no prolems on the mtb trails with the 28, but have a 70 km race where the very last hill is brutal. Barely made it last year and wanted to make my life easier.

Makes sense, more gears on the back can be nice at the end of a long ride, what is a gentle climb on a normal day can be killer at the end of a long ride