I'll take a shot at it. Fair warning, there is a lot of guesswork! This is a hypothetical rocket that will probably never get built. Nevertheless, this should help us get a sense of the class of payloads a Falcon 45 could loft.
Unlike the final speed of a rocket, which is an exponential problem, you can get linearly more payload by adding extra rocket. (ie, if you want twice the payload theoretically you can just launch 2 rockets).
I will therefore make the following dangerous assumption: Making a Falcon Superheavy by adding two boosters to the falcon heavy will have the same linear affect on payload as making a Falcon Heavy by adding two boosters to the Falcon 9.
Low Earth Orbit (LEO):
Falcon 9: 22,800kg
Falcon Heavy: 63,800kg
Approximate Superheavy LEO payload: 100,000kg $\approx$ 63,800kg + 41,000kg
Geostationary Transfer Orbit (GTO):
Falcon 9: 8,300kg
Falcon Heavy: 26,700kg
Approximate Superheavy GTO payload: 45,000kg $\approx$ 26,700kg + 18,400kg
Trans Lunar Injection (TLI):
Falcon 9: ~7,000kg (This is a guess between GTO and TMI payload)
Falcon Heavy: 23,400kg (Based on PearsonArtPhoto's work here: What is Falcon heavy's payload capacity to Trans-Lunar Injection)
Approximate Superheavy TLI payload: 40,000kg $\approx$ 23,400kg + 16,400kg
(Fun fact: Apollo Command Module+Service Module+Lunar Module is close to 50,000kg, and the Orion Crew Vehicle is about 26,000kg)
Trans Mars Injection (TMI):
Falcon 9: 4,020kg
Falcon Heavy: 16,800kg
Approximate Superheavy TMI payload: 30,000kg $\approx$ 16,800kg + 12,780kg
Trans Pluto Injection:
Falcon 9: 500kg (This is a 100% total guess. For all I know there could be a shortfall)
Falcon Heavy: 3,500kg
Totally guessing Superheavy Pluto payload: 6,500kg $\approx$ 3,500kg + 3,000kg
Take this all with a grain of salt; there are a lot of reasons these numbers could be wrong. For example, the four boosters would probably need to throttle down a lot more (hurting payload), the center core might need to have even further strengthening (hurting payload), and the center core could possibly have its engines started well after launch to conserve fuel (helping payload).
Additionally, to lift anything more than 11 tons to anywhere, the Falcon's Payload Adapter Fitting (PAF) would need to be upgraded (this is also a problem for Falcon Heavy). Fairing volume would likely also be an issue for such heavy payloads.
What is Falcon heavy's payload capacity to Trans-Lunar Injection