certainly, the support of the Egyptian Navy, which far outclassed the Roman one during this time would be boon sent from the heavens for Carthage.
The problem is however that already since the Laenas - Antiochus V showdown in front of Alexandria in 167 BC, the Ptolemaic realm has fallen to a large extent in the Roman sphere of influence. There was also the ever-present threat of Ptolemy Physkon, his brother, who was , in 149 BC, twice defeated in civil wars against Ptolemy VI and left to rule Cyrenaica under the close supervision of his brother, but still retained his ambition to sit on the throne; furthermore, he has most likely maintained good relations with the Romans - who had helped him in 155 BC in his unsuccessful attempt to capture Cyprus and who had received his will that bequeathed his territories to Rome if he died without an heir rather favourably. Then there is the unstable situation in Syria, where Alexander Valas is doing his best to piss off everyone and the Seleucid realm is disintegrating; Ptolemy would have to pay attention there, for Demetrius, the son of Demetrius I is still alive and plotting to return and the situation can allow Alexandria to reclaim Coele Syria.
So I think it would be very hard for Ptolemy VI to risk that much; it would probably take a very hostile Rome, especially towards him and a Rome which can't exactly intervene in the East, especially east of the Aegean. This could be achieved perhaps if the Romans had been overbearing in the late 150s BC., perhaps pressuring Ptolemy VI to accept Physkon as his co-ruler instead of designating him a subordinate king in Cyrenaica. Constant Roman meddling in that period, perhaps the result of Physkon maintaining his infleunce on the Senate, which may be considering the rather incompetent Physkon a better candidate for the throne than his more energetic and potentially independent-minded brother (similar to the plans to place Valas on the Seleucid throne) could perhaps, over time, push Ptolemy VI more and more to a - still concealed - anti-Roman stance. The outbreak of the Punic War then splits the Alexandrian court, as Philometor (Ptolemy VI) is leaning towards covertly supporting Carthage for he fears that without that distraction, Rome will soon turn its full attention to the East, threatening his position and even his life, while Physkon, ever the Romanophile, wants to actually enter the war on the side of Rome. Perhaps after the first reversals in Africa, with the Roman attacks repelled, the Romans decide to try to draw the Ptolemies in the conflict, by having them cut all ties with Carthage, provide bases for the Roman fleet and perhaps even join the war. Philometor's visible unwillingness to accept these request, especially the war on Carthage, makes the Romans very suspicious about his intentions and they start perhaps to prepare the ground to make Physkon king. In this case, they try perhaps to have the newly crowned Alexander I of Syria, who owes his throne on Roman support, to support Physkon in a bid for the throne. After an alleged attempt on his life, Physkon suddenly absconds and heads to Cyrenaica where he starts to raise a mercenary army in order to be able to join Valas on his operations and force his brother to fight on two fronts.
However, the plan unravels when the Jews, under the command of Simon Maccabee ambush the Seleucid army and inflict heavy losses, forcing Alexander to retreat and abandon the campaign, allowing Philometor to defeat his brother before his preparations were completed (and ordering his execution in order to end the incessant trouble coming from him, despite the strong protestations of the Romans). The defeat discredits Alexander Valas, as the kingdom starts disintegrating and soon afterwards, the son of Demetrius I, now Demetrius II returns from Cnidus at the head of a mercenary army. Alexander's position seems to be seriously enadangered; however, the prospect of the son of Demetrius becoming king and potentially resuming the policies of his father as well as losing influence in the Seleucid kingdom worry two of the main pro-Roman forces in Asia Minor, Pergamos and Cappadocia, leading Attalus II and Ariarathes V to intervene in the conflict on side of Valas. With Pergamenese and Cappadocian support, Valas manages to defeat Demetrius, who dies shortly afterwards, perhaps by the hands of his mercenary commanders. Thus Alexander I has secured his position, but only temporarily so, for Ptolemy VI has turned his attention to Syria, realising that Valas is no longer a friend of the Ptolemaic dynasty and a real threat to his rule. Exploiting the resentment created by Valas' continuous persecution of real or alleged supporters of Demetrius II and his mismanagement, in the spring of 148 BC. he marches north. With his army disintegrating and senior generals of his abandonign him and joining the ranks of the Ptolemaic army, Valas initially retreats to Cilicia, attempting to raise a new army and march on Antioch. However, his calls for help are returned unanswered, as Attalus II has to deal with the dynastic problems in Bithynia and Ariarathes, considering him all but done, remains neutral; soon, he is besieged by Ptolemaic forces in Mopsuestia, dying in an attempt to break through the enemy lines.
With this, Ptolemy VI is left in control of the Seleucid kingdom and he starts trying to settle the affairs there in a manner that would serve his interests. His main objective is to be able to reclaim Coele Syria from the Seleucids and place a dependable figure on the throne; however, there is growing pressure for him to wear the "diadem of Asia" for himself and claim control of the Seleucid patrimony. The Roman Senate is vehemently opposed to this and requests that Ptolemy not take the crown and instead recognise the young brother of Demetrius II, Antiochus (Sidetes) as king. Ptolemy however is unwilling to abandon his favourable position before securing guarantees for his kingdom's and his own safety. Interpreting this as a wish to repeat Antiochus IV's plan and unite the two kingdoms under Ptolemaic rule, the Senate preemptively recognises Antiochus as Antiochus VII and orders Ptolemy to withdraw. However, this time, with Rome still not havig dealt a decisive blow on Carthage, dealing with rebellion in Spain and with Greece nearing a state of insurrection, Ptolemy decides not to back down, thus leading the Senate to declare war on him.
Tbh, I don't think this is a very plausible scenario. Being potentially overstretched, the Romans would probably not go too hard on Ptolemy VI and they would probably accept a deal where Coele Syria returns to the Ptolemies with Antiochus VII ruling over the rest of the Seleucid territories and being controlled by the Senate in order to prevent a potential conflaguration with Egypt at the time. But, at least according to me, it is perhaps the best way to get Ptolemy VI at war with Egypt and in a position where he can perhaps pose a credible threat and try to actively help Carthage if possible.
(I hope I didn't make any mistakes)