The Simple answer is Yes you can assemble an 11-36t 9 speed cassette, most easily by changing the bottom 12t sprocket on an HG-61 for an 11t…
But I’m not sure there is that much advantage in doing this, you could just opt for an 11-34 – 9speed off the shelf cassette and “Nut up” for the lack of 2 teeth…
My own current lowest available ratio is 30-22 at the minute about 19 “Gear inches” That gets used very infrequently and TBH is probably a bit too “spinney” – 36-22 would come out a shade under 15.9 and 34-22 works out at 16.8 the gains would be minimal…
Perhaps your easiest, short term option is to get an 11-34 9 speed cassette just to try having a broad range cassette and see how you get on with it…
Don’t get too caught up with the idea of having 10spd kit on your bike, it’s just the latest gimick all the old 5/6/7/8/9spd kit hasn’t suddenly ceased to function.
There are far better things you can do with your Bonus….