I have spent a LOT of time over the years working on Paradiddles and Paradiddle Inversions. What I haven't spent as much time on, is Double and Triple Paradiddles.
So, quick review.
Double Paradiddles are RLRLRR LRLRLL so if we want to play them in a very "consonant" and non-over the bar way, they work great as triplets or in 3/4.
Triple Paradiddles are RLRLRLRR LRLRLRLL (although we could certainly start both of these rudiments on the left hand as well.) This sticking adds up to a bar of 4/4 on each side of it, so that works quite well to start with.
Here are a few ways I used these rudiments. Most of them voiced around the drum set and quite a few of them going over the bar. Note I didn't film most of these or even write them out, but you will benefit from filling in the blanks on these yourself, as well as coming up with your own ideas.
1. Triple in 8th notes in 3/4
2. Triple in triplets in 4/4 and 3/4 (add whatever foot patterns feel represent these time signatures).
3. Doubles in 8th notes in 4/4.
4. Doubles and Triples in 8th notes in 4/4 w/ dotted 8th notes in bass drum.
5. " "" in hi-hat. ( BD plays quarters)
6. 4-5 in Triplets
7. 4-6 in 3/4 time.
8. 4-7 with 7 beat on again/off again BD pattern.
So, as usual, there's tons of work to do.
We can also play with putting in accents that don't naturally go with the stickings. Try playing double paradiddles in 8th notes in 4/4 but only accent in half notes. Or here's a fun one. This is a Triple Paradiddle w/LH on snare and RH on hi-hat with dotted quarter accents and a 2-beat feel in the feet. It has a sort of relentless feel that I like, and seems to get more powerful the quieter I play it. As always, play for the music and be kind and gentle with yourself.