Can you have a cassette like 11-12-13-14-16-18-21-24-36? What's the biggest jump between sprockets that will still shift ok? Chainrings are 26-36-48. I'm thinking of a more roadish/commuterish cassette, but with a last resort super sprocket if I suddenly find myself offroad or doing some ridiculous hill.

Sram has 10-speed cassettes of 11-36 and 12-36 and 9-speed 12-34s. Shimano has 9-speed 11-34. None of them have a 24T second biggest cog, though, more like a 30.

Shimano 8-speed megarange have a big jump on the biggest two cogs.

You'll need a derailer that can cope of course.

First of all, what kind of setup do you have? You asked about a nine cog cassette so is it nine speed?

I would suggest that you go with a regular 11-32 or 12-36 cassette for nine speed. The gaps are close enough that you're not constantly shifting the front to find the in-between gear ratios.

The whole point of the Megarange cassette was to have closer gaps on the smaller cogs. With 8 speed a regular wide range cassette isn't that bad (you still shift up front more) but with a 7 or 6 speed you'd end up with gaps big enough to drive a truck through. The Megarange cassettes just aren't necessary with 9+ cogs.

Keep in mind that if you're probably going to need a long cage derailleur when going to a wider range cassette, if you don't have one already.

many cassettes fix the larger sprockets on a core of aluminum as a group,
to save weight,
but that disallows a custom combination ..

12 tooth jump? Probably. Only one way to find out. Some Megarange 7-speed freewheels had a 24-34 jump, I had one and it shifted just fine. You will need a mountain RD with the b-tension screwed in quite a bit if you want to run a 36T.

Do you really need 26/36? I'd rather put a smaller ring on the granny rather than shifting from a 24 to a 36, your feet might not be able to keep up with how much you'll have to spin that tiny gear/huge jump. Or something more reasonable like a 32T largest cog.

I definitely need it - I'd go lower if I could. I have a nasty habit of touring off road up ridiculously steep hills. There are still hills where the only thing stopping me is the lack of an even lower gear...

And a longer chain.

Shimano 8-speed Megarange cassettes jump 8 teeth, 26 to 34, has some pretty pronounced ramping, and requires a Megarange-capable derailleur. In my 38 years of cycling I've never seen a rear derailleur handle a 12-tooth jump. And every 8-, 9-, and 10-speed cassette I've seen bolts, rivets, or swages the three largest cogs together. There's probably a reason for this.

You're pushing into uncharted territory. I'm not saying you can't make it work, just that after disassembling two or three cassettes to get the the cogs you want you might find that your derailleur still can't handle it.

I know from experience that older 6 & 7 speeds will take a couple of 3 cog jumps and 4 at the end to get you to a 32 or 34 a lot of vintage Schwinns had this type gearing. But you don't need it for most type riding a basic 13-28 or 14-28 is all you really need. Basically on a derailleur your limited to a 4 cog jump on road DR's and maybe 6 on long cage MB anyting more is going to have problems.

These can be easily disassembled or defeated with a dremel tool (rivets.) The purpose is to make the cassette stiffer, easier to install, and (to a certain extent) not tear up the freehub body. I have never had a problem running loose cog cassettes on steel Shimano Freehub bodies. Cheap aluminum knockoffs, probably best to leave those rivets intact.

Have to disagree here. I'm currently running a 21-28 jump on my road bike (7 teeth) with a Shimano 600 tri-color short cage RD. It indexes just fine. Maybe I will put a 30 back on there and see if it will do a 9 tooth jump. (I already know it will handle the 30T.)

Except for the SRAM 12-32 with 12-13-14-15-16-17-19-21-24-32 which lets compact double riders with 10 cogs have the same range and gear spacing in the cruising range they had on a 53-39-28 x 13-14-15-16-17-19-21-23-26 9 cog road triple but with more double shifting and fewer SKUs for SRAM to make/stock/etc.

I have done similar gear jumps and had them work OK the problem is the user needs to shift correctly. Which is something that won't happen with the majority of users.

No Campagnolo 8 speed cassette has any cogs attached together.

Campagnolo Veloce and below 9 speed cassettes have all loose cogs. Chorus and Record Mk II cassettes have the 2 largest pairs (11-21/11-23), 3+2 largest, or 2+3 largest cogs on carriers.

Campagnolo Veloce and below 10 speed cassettes, 2010 Centaur, and newer Centaur 14-23 cassettes have all loose cogs. Other Centaur setups put the two largest cogs on a carrier. Record and Chorus put the 2 (21 and 23 ending cogs) or 3 largest pairs on carriers.

IRD Comp cassettes have all loose cogs.

Miche and Marchisio cassettes have all loose cogs.

Shimano CS-6500 cassettes in the 13-23 and 13-25 combinations have the last cog loose. The 14-25 has the last two cogs loose.

Etc.

Cyclists who can weigh 200 pounds obsess about an extra 20 grams of weight on their cassettes and are willing to pony up extra money to have the big cogs mounted on aluminum carriers. Vendors cater to that mentality and compete against each other on weight, with replacing steel cog centers with aluminum a low cost way to gain some grams.

Aftermarket aluminum Shimano freehubs also get dented by loose cogs because the splines aren't deep enough to allow the softer metal to work.

What type of crank do you have?

My replacement cassette for similar reasons is a 9sp 12,14,16,18,21,24,28,32,36 and I run a 52-42-26 up front. I don’t miss the 11 in the back at all with the 52-42 combo. Personally when I get in the 26 up front I like having more of a range in the back than just the 36. And the shifts between 24,28,32,36 are all easy. That gives me a range of granny gears between 29 and 19 gear inches.

Around here there are some steep hills also that I needed lower granny gears for but as someone mentioned you can also spin yourself out with that 19 gear inch when the incline drops off a little and having a 22 and 25 gear inch in between that 29 will make those shifts under load a lot easier IMO.