Falcon 9 was improved by adding 2 side boosters - making Falcon Heavy. Would there be a significant benefit from adding ... say 2 more boosters?
(I'm dubbing this Falcon Super Heavy)
At the moment, not really. The payload adapter that SpaceX has in service has two versions. The largest can only handle 23,000lb payloads.
Thus the 63 Metric Tonne (expendable, less reusable) number, is sort of theoretical with the current PLA. Now of course developing a better PLA is not as hard as adding two more boosters. But no one has shown interest in it yet.
Additionally, the current fairing is too small. It is volume limited. Sure it is quite large, but payloads of the size of 63mT or bigger could really use a larger payload fairing.
They cannot easily make it much longer, because the fineness ration is already pushing it on the Falcon 9 booster. (It is very thin and long, and there is a limit of how much longer they can make the stack and not bend it or keep it stable in flight).
They cannot make it too much wider (probably somewhat), it already is a 5m fairing on a 3m core, so it hammerheads out over the edge about a meter on either side already.
Musk himself has acknowledged that the Heavy in hindsight was not the greatest idea. It is useful, serves a purpose, but the BFR will eclipse it very soon. (Especially if they are testing the BFR first stage with Grasshopper like missions in 2019).
Elon had teased about the Falcon Super Heavy when discussing the powers they could put into their rockets:
“We could really dial it up to as much performance as anyone could ever want. If we wanted to we could actually add two more side boosters and make it Falcon Super Heavy,” Musk said
Here are four things we learned from Elon Musk before the first Falcon Heavy launch - The Verge
The article goes on to claim that the rocket would be able to reach 9 million pounds of thrust, almost double that of the Falcon Heavy (5.13 million pounds of thrust). This increased thrust would allow bigger and heavier payloads to reach various orbits.
SpaceX have reported that the Falcon Heavy was more difficult to develop than they had expected, essentially due to the extra demands on the central core and control systems from the different thrust loads and vibration from the boosters. Presumably adding two more would make things even harder. Also you'd probably want to throttle back two of the boosters after launch until the other two had separated (so that the fuel in the remaining two is not wasted accelerating the first two), so now you have boosters needing to be string enough to be pushed by other ones....
In summary, it would probably be too hard. It does seem in rocketry that the straightforward "pod on a stick" design is awfully hard to beat.
The Falcon Heavy uses 27 engines at launch, 9 engines after booster separation and one engine in the second stage.
A Falcon "Super Heavy" with 4 boosters would use 45 engines at launch. It might be necessary to separate two boosters earlier than the remaining two to limit the maximum acceleration. A different second stage with more than one engine and larger tanks should be used for the larger payload. A stronger structure of the core stage and the second stage is necessary for the increased payload mass. Another payload adapter and fairing for larger and heavier payloads.
There should be a certain relation between the thrust of the boosters, the core stage and the second stage. If the number of boosters is increased, some modifications of the core stage and the second stage are necessary. Not only in adequate thrust but also in tank volumes and structure strength.