'Implausible Scenario:
Tiberius Gracchus Triumphs'.
Land claims to the
ager publicus are restricted to 500 iugerta (~1.2 square kilometers), most probably with an expansion of another 250 iugerta for the owner's son, that expansion being limited to two sons. In other words: a family can retain at most 1000 iugerta, or roughly 2.4 square kilometers. (The exact mechanism by which this 'expansion' would be regulated is disputed, but since Tiberius was heavily pro-natalist, we may assume that the land in excess of 500 iugerta may only be retained by any owner if he has sons. If only one son, then 250 iugerta revert to the state; if no sons, the additional 500 iugerta fully revent to the state, and only the 'official' maximum of the base 500 iugerta may be retained.)
All the land that is thus freed up -- and indeed, all 'public land' -- is (re)distributed to the landless Roman citizens, first and foremost to veterans. Various allotments have been mentioned. Commonly cited is 30 iugerta a man, but we should consider that usually in colonisation efforts, 10 iugerta a man was the regular offer. Three times that seems improbably excessive. For my money, Tiberius was probably just willing to give more land to 'deserving' allies of his cause, and since he'd be in charge of the commission, he'd essentially be quite free to decide who got how much. Let's say that an average of 20 iugerta per capita is quite plausible, then.
Now, officially, the
ager publicus was precisely that: held in common on behalf of the public. This was not the reality. Tiberius would exploit this by putting rent on the land, crafting a construction whereby the land was in practice owned by the private citizen who held it, but it was held as
part of the 'public land', to they had to pay the rent, otherwise the land would revert to the state. This would generate income for the state.
The tenants would be happy regardless, since the land grants would elevate them from a landless underclass to land-owners who met the property qualifications for military service. Many extended families, rather than having perhaps one scion who rose to that rank, would see several of their sons rise to citizen-soldier.
Conversely, a few of the aristocratic houses would be broken, having leveraged their expensive loans against the (presumed) income from their land-holdings. Many more would be not
broken, but would still receive a major blow. Similarly, the Socii (the allied Italian peoples, beholden to Rome) would be eviced from the land as well; which is why they were among the fiercest enemies of Tiberius Gracchus. They were whipped up in this, to be sure, by the aristocratic enemies of the Gracchan plans-- and we should note that a decade later,
Gaius Gracchus made several provisions that would allow certain groups of Socii to share in the envisioned land distributions. (Specifically, those willing to support the Gracchan faction could gain citizenships and land grants in exchange for simultaneously signing up for military service. This was essentially a 'pilot version' of what Gaius Marius would implement on a grand scale, three decades further on.)
We may assume that in a Gracchan victory scenario, the Gracchi would also implement such provisions, although I don't think they'd implement it across the board, like Marius would in OTL. Their faction was still very much that of the lower classes of the citizenry, and their electorate viewed the Socii as squatters on land that should rightly go to honest Romans. So while certain pro-Graccan groups of Socii could be made into "new citizens", a delicate balance would have to be struck.
(In OTL, the general thrust of Gaius's reform in that gerdard was to give citizenship to the Latins, and to give the Socii the traditional rights of Latins, thus elevating both 'by one step', as it were. With the previous reforms of Tiberius enacted fully and without compromise, the Socii would be hit harder, so I can easily see additional 'appeasements' by granting outright citizenship to some select Socii, as I have outlined.)
The more radical reforms of Gaius Gracchus in OTL would probably be averted or 'softened', in this ATL climate where Tiberius is successful (and also actually has to
govern). I do think that the Gracchan plan to establish public granaries would still be enacted, so as to secure the food supply. The road-building programmes advocated by Gaius Gracchus in OTL would also be implemented (with the contracts, preicatably, handed out to Gracchan allies). Similarly, the military law to provide soldiers' clothes from the public treasury would be enacted (whihg, again, would make the military more accessible to the supporters of the Gracchi).
Within some years (considering that Gaius realised this a decade after Tiberius was killed), the Gracchi would find that there wasn't enough public land in Italy to provide for all would-be receivers of allotments. In OTL, this promted Gaius to begin sponsoring clonies of citizens otside the peninsula-- then a novel approach. I'm confident that the same holds true in this ATL. Presumably, with the land reforms being enacted more extensively and thoroughly, this point is inevitably reached earlier. Taking more land from the Socii will eventually just become impossible... at least without sparking an early ATL version of the Social War. This will cause the Gracchan faction to begin the establishment of overseas colonies, presumably beginning (as in OTL) with their much-advertised plan for a Roman colony at Carthage.
Establishing these colonies, and having opened up the military to a lot of families (consisting of their supporters), there would be a serious outflow of soldier-settlers to the "Gracchan colonies", thus really hastening the growth of the Roman citizen body outside of Italy, compared to OTL. (Here, too, they may well find an eventual solution to the problem of the Socii: offering many of them citizenship and land
in the colonies, in exchange for military service.)
Now... would this save the Roman Republic? I daresay that it might. It wouldn't remove all the problems, but it would avert the Social War, and give Rome a demographic and military edge in the decades of wild expansion ahead (compared to OTL). The interests of the OTL (to-be-formed) Populares would be well-served, and the power of the Optimates would be broken before they even had a chance to coalesce properly. This would in turn prevent the Populares from being forced into an embittered vendetta caused by structural marginalisation. The result being that Roman politics would be far less poisoned. (And, of course, the OTL precedent of the Gracchi being murdered wouldn't be there.)
There would still have to be significant organisational reforms, both of the military and of the political structure. The fact is that the traditional institutions of the Republic were originally suited to the governance and defence of a city-state; and were not equipped for the administration and the wars of a burgeoning empire. In this ATL, that empire may truly remain a Republic, but it will be a reformed one. Not that this would be unthinkable. With the Socii matter handled already, and the more obstinate aristocrats out of the way, an ATL counterpart of Gaius Marius should be able to see to it.
And a hundred years after the triumph of Tiberius Gracchus, an ATL counterpart to Gaius Iulius Caesar -- already a decade older than he ever got to be in OTL -- lives a relatively quiet life, the great matters of state having been solved decades before his heyday. (Or, you know, maybe ATL Caesar uses the fact that no civil wars are required in order to totally crush the Persians and annex Mesopotamia or something.)