This is a very interesting idea, to which I really wish I had more concrete to contribute than I do. I actually have years of experience with agricultural co-ops... too bad I was generally under 12 years old for most of those years! My father was the president of our state’s wool co-op when I was a kid, and managed another co-op. Anyway...
If the goal is for these co-ops to supplant the latifundia on an economic basis, particularly with cash crops, I think thats quite a challenge, because of the degree of expertise needed. If we’re talking focusing on your normal crops and livestock, it should be easier. Not subsistence, mind you, but it took professionals to run the latifundia (not that they’re the senators themselves, but sometimes, they were), and plenty of resources. Senators could afford to adapt to economic changes, and were in a better position to do so. They have better networking (Senator Quintus tells me he’s had success growing olive trees in this fashion), better access to market info (We’re going to war with Persia next year, lets plan accordingly), and were, all around, better equipped to succeed at managing latifundia.
That isn’t to say that these co-ops couldn’t succeed, they certainly could. The Roman legal system could very easily adapt to co-ops, they had collegia, also known as corporatio, which were organizations with the sort of legal rights we associate with corporations today. They could hold property, and their membership could change, which are the two main things we’d want here. The main restriction (besides needing to be approved, legally) was that each had to have at least 3 members, which is no problem in this case (in fact, you’d probably want it higher for these). So, just to give it a suitably latin name, we call this type of co-op a ‘collegium agriculturae’ (if my rusty dog latin and checking with google translate at half past midnight are correct). So, there’s a huge plus: this would make sense to the Romans.
Even if these collegia are not as rich as Senators, they can still probably afford the basics. They could support their own mills, presses, and other such infrastructure needed. They might not be as well educated as the Senators, but, with a large enough pooling of years and generations of knowledge, it won’t really matter if they haven’t read Pliny’s latest works on Natural History (though, to be fair to the Romans, they did tend to have high literacy for the times), each collegium will have enough collective knowledge to be pretty well equipped to have a diversified agricultural set up going. They could probably also afford slaves (owned by the collegium), and overseers, particularly if this is in a period where slave prices are low. So, will they be as super productive as the latifundia? Probably not. Will they be economically viable? My gut says yes, without considering the possibility that the government might subsidize them to some degree. A likely eventuality, as the senators try to figure out how to tap into these collegia, is that they could contract work out to them, not unlike how much big agro-biz can work today. Senator Quintus promises a price of x denarius per amphora of wine, regardless of economic conditions. The collegium gets the security of a set price based on their output, the senators get to leverage their economic clout.
I would imagine that there would be some pretty strict rules about establishing these and about maintaining them, particularly if their purpose is to help weaken the senators and ensure that the small farmers aren’t run off their land, and that veterans don’t come home to find they’ve been evicted. First of all, you’re going to want to make sure that each collegium is large enough to absorb losing men to war, without the whole thing going under. That also means that, when first set up, you’re going to want to have a diversity of ages, and as many family men as possible. This last part is doubly important, since you’ll need kids working the farms while their dads are away, and you’ll need wives to keep the men that say behind from making sure the wives of those at war don’t feel too lonely. Old men can farm, but they don’t often go to war. Further, having a variety of ages allows you to have a variety of skillsets.
You’ll also want to make sure that everything in their establishing charter is very explicit and thorough (good thing we’re supposing this is a Roman endeavor!). You don’t want anyone coasting off the efforts of others (a very common problem with collective ownership), so you’ll want something to be owned privately, in conjunction with property owned by the collegium. I would suggest that any given man’s land should be technically held by the collegium, but whatever he produces from the land is his (minus his dues to the collegium, for the common expenses). Perhaps you could have something a bit more sophisticated, where each plot of land is owned by an individual, in cooperation with the collegium (in other words, owned by a collegium composed of the farmer, a relative, and the main collegium itself), but that might be a bit too complicated or sophisticated for the era. Basically, you want to ensure each partner has the maximum freedom over ‘his’ plot of land and what to do with it, while also making sure that the collegium can’t be broken up and sold off, bit by bit. You’ll also need specific means to handle what to do with the farmer is off fighting in the legions. Who farms ‘his’ land, and what obligation does the collegium owe to his family? Also, inheritance is important. Does a son automatically inherit his father’s ‘lot’? How about multiple sons? Can lots be combined? All of this needs to be properly spelled out ahead of time, you want these to endure. You also want it to be pretty straight forward, so you don’t need jurists from the capital swinging by constantly to make sure that everyone understands how this works. Speaking of the legal structure of the collegium, you’ll want its charter to be explicitly dependent on the Emperor’s good graces. This is Imperial Rome, after all, the civilization which, under one of its greatest Emperors, Trajan, thought that private fire brigades were too great a risk to the government.
I’m sure there’s more details to consider, and this really is a cool idea, but one last addition: I know the OP requested something after Augustus, but isn’t this perfectly suited to the Gracchi?