The way we do this is start on the ground. We do some stretches from yoga that are relevant to the muscles used in grappling, then play some moves and transitions as a warmup. Then we pair up and play pins. We use the Newaza from Judo and the basic ground moves from Brazilian Jujutsu as they complement each other perfectly and don't leave any gaps.
Each pin has an escape and we play these, also drills such as pass the guard-escape the mount. Then we look at finishes from each position - chokes and locks. Then we look at the counters and reversals.
Then we stand up and look at throws, simple moves from Judo and wrestling such as Kata guruma - cross hip, seoinage - flying mare, o soto gari, simple stuff like that, so we know how to get there, and moves such as morote gari and other leg takedowns, and how not to get caught in the guard. Also pad drills on the ground, punching the pads while in the mount and guard.
Then by adding back in strikes to vertical grappling, the Thai clinch drill, and HKE, we can progress to kickboxing on the mat, and from the clinch, go to ground, practice ground and pound, and grappling.
With the new mats at the club, we can regularly explore grappling, MMA and Vale Tudo, and devote maybe an hour from a 2 hour class to this dimension of our fight training.