For (additional) caravan requests, I'd say that using renown to judge if the requestee would honour the invite would then lead onto a trial caravan (sized according to the degree of said renown) whose return (and later size) is predicated upon how worthwhile the trip was, each time, so that loss-making trips would dial down enthusiasm and even lead to the cessation of visits.
(Might be worth making the 'traditional' three caravans, after the compulsory tentative stab at visiting the newly-(re)founded colony, respond more flexibly than currently. With the exception of who initiated them, they could have effectively the same susceptibility to altered enthusiasm as invited traders after a few years pass, for better or ill.)
With >4 caravans (or >3, assuming¹ still no winter one) two or more caravans could be arriving at the same time during (at least one) season, or at least with significant overlap. That would alter 'trader mood', too. Perceived lower utility might nark them, but (assuming simultaneous
or parallel Depot visits) opportunities to inter-trade between themselves might be something their respective origins would be pleased with. If we changed from the Depot system (or added to it) by assigning a Trading Zone then a "Wagon Back Sale" could form, each wagon lining up on the designated site and forming a temporary 'shop' workshop to be frequented by all who pass by.
A seasonal market that becomes popular (
e.g.) might gain an inertia of its own, beyond one's actual control, organised outwith your own diplomacy skills (and
maybe producing other problems, like trader rivalries or cheaters and sneakers of various kinds, from within and without your base site civ, who need extra-cateful management before the fact and punishment after it). You'd be competing against
other local hubs (as we've seen, market hubs are a worldgen thing now, just ripe for at least
influencing in Fortress Mode site management and conscious improvement) and renown/inhospility in trading might influence other site factors (e.g. more/less sieges, according to various motive-hooks determined as armies march around).
Many possible things we could do. A lot of them probably needing a lot of complicated coding (or recoding) to accomplish. But so much
flavour!
¹ A
big assumption - Imagine a regular winter trading opportunity, even
tied to the Trading Zone atop a frozen river...