Leverage the dichotomy as a brand. Endless promotional opportunities.
We only sell pineapple pizzas*
*well, we sell the other ones, but they are not as nice
The fun pizza brand. Cheap and cheerful. Maybe partner with SpongeBob…
So the main menu, everything has pineapple, and that is the only ingredient that cannot be removed or changed. This is spelled out majorly. The other menu, maybe named something insulting, offers non-pineapple regular pizzas, and the impression will be that it costs more to be a pineapple hater. Reality is they undercut competitors on price regardless.
Cheaper because there is less cheese. From making pizzas at home I have found that less cheese and a flatbread base can still taste awesome.
Healthier ingredients. Fewer cured meats (pepperoni, sausage out, bacon and ham stay but in reduced amounts). Chicken takes priority. Premium flatbread option (like +$2) for lower carbs, bit might require its own oven machine.
Healthy sides and drinks. Again, healthy is cheaper, but unhealthy is still competitive on price. Think kombucha vs coke.
Push sides heavily. They tend to be high margin. Make awesome garlic bread (not like the cheapest from a supermarket), three types of fries (not oven baked), and lower markup drinks. Turnover from greater perceived value.
Dynamic pricing. Chains already do this by sending out offers outside of weekends. Do this, but that is simplistic… make it more like Uber and when pizzas can be had extra cheap, alert the customer base. Just make sure it feels special and not every weekday.