Yes, many times, and often when they weren't actively being invaded, Egypt was still meddling in their affairs.

The story of Shishak, specifically, is a difficult one to confirm in history because of the presence of the Hebrew king, Solomon, who is regarded as a mostly legendary character by historians. Based on the chronology offered by 1 and 2 Kings, and the corresponding chronology from Egyptian documents, the most plausible historical identity is Pharaoh Shoshenq I. We don't know much about Shoshenq unfortunately, so it's basically impossible to confirm or deny the Biblical narrative. Egyptian pharaohs regularly invaded the Levant, so it's entirely plausible that Shoshenq could have as well, but very few records remain from his reign. We can say that the Bible indicates that Solomon lived around 940, and Shoshoenq was Pharaoh in that same period.

On the non-invasion end of things, 2 Kings 17 covers the reign of Hoshea, the final king of Israel/Samaria who was conquered by the Assyrians and references a Pharaoh named "Sho," who is hard to identify. Conventionally "Sho" gets associated with Pharaoh Osorkon IV, but could also be and abbreviated version of "Shoshenq V." Many ancient cultures would occasionally abbreviate the names of foreign rulers like that, and the Egyptian succession chronology around that time (c.730 BC) isn't well established. Regardless of the specific Pharoah, 2 Kings explains that Hoshea had been a vassal of Assyria but rebelled because he expected the Egyptians to invade and back him up. They didn't, and Assyria conquered the northern Hebrew kingdom.

Both 2 Kings 19 and Isaiah 37 refer to an invasion by "Tirhakah, king of Kush" in the reign of Hezekia in Judah. That neatly corresponds to Pharaoh Taharqa of the 25th Dynasty, except the Biblical and Egyptian chronologies don't align on this one. This Pharaoh invaded Judah, which remained an Assyrian vassal, to support several of his own vassals in their rebellion against the Assyrian king, Sennacherib. Based on 2 Kings 19, this should have been in 701 BC, but Egyptian records don't place Taharqa on the throne until around 690. "Tirhakah" doesn't fit with any other Egyptian or Nubian name, and the events described are completely inline with the Egyptian and Assyrian histories of that period. The most likely explanation for the discrepancy is a simple error on the part of the author of 2 Kings, or even their scribes. It could be a mistaken regnal year, or it could be a mistake over which Pharaoh was ruling at the time.

The last major Biblical invasion by Egypt is also possibly the most famous. Taharqa's war against Assyria (and Judah by extension) failed. Over the course of several invasions in the following years, the Assyrians conquered Egypt and placed a new "Egyptian" (technically acculturated Libyan) dynasty on the throne. The new 26th Dynasty maintained a close alliance with Assyria, and when Assyria was on its last legs in 609 BC, Pharaoh Necho II used that alliance as a pretext to march north. The Assyrians had already been all but destroyed by a coalition of Babylonians and Medes who had destroyed their capital and hounded them to a Syrian outpost called Harran, where the Assyrians were defeated once and for all.

Necho was not able to reach them in time for a few reasons. A) He probably didn't actually want to and just used it as a causus belli. B) In a bid for true independence, King Josiah of Judah led an army out to face Necho as the Egyptians were marching through Judean territory at Meggido. Josiah was killed in battle, and Necho continued on his way. On his way back a few months later, Necho threatened to do it again and deposed Josiah's son without a fight. Over the next 4 years, Egypt and Babylon sparred for control of the Levant repeatedly, but the Babylonians ultimately won and pushed all the way to the Sinai.

That conflict between Egypt and Babylon ultimately set the scene for Judah's own conflicts with the Babylonians. Many Judean nobles and kings saw Egypt as a more appealing benefactor, while others like the prophet Jeremiah were pro-Babylonian. Around 601 BC, King Jehoiakim pledged tribute to Babylon, but by 598 the pro Egypt camp had won out, sparking the rebellion that ended with a siege of Jerusalem and the beginning of the famed Babylonian Deportation. 13 years later, King Zedekiah of Judah made an alliance with Pharaoh "Hophra" according to Jeremiah. Through some linguistic quirks of Egyptian, Hebrew, and Greek that corresponds correctly to Pharaoh Apries, who had already antagonized the Babylonians. Jeremiah says he expected some kind of aid from Egypt, but it never came and Jerusalem fell to Babylon.

The Jews were returned from their exile by the Persian Empire after they conquered Babylon 14 years later, the Persians conquered Egypt too, but in 404 BCE Egypt broke away. One of the early Pharaohs in this period, Hakor, supported several rebellions against the Persians in the Levant. Based on some scant evidence from the Jewish historian Josephus, some historians suggest that he, or the later Pharaoh Nectanebo II, may have tried to instigate one in Judea as well, but it was clamped down on by the Persian authorities.

At least one of these interim Pharaohs, Teos, may have planned on invading/annexing Judea around 359. He sailed to Phoenicia with a Greek mercenary army but was betrayed and assassinated upon landing. Given that Phoenicia was north of Judea, any military success would have cut the Judeans off from Persia and pulled them into the Egyptian orbit.

Then there's the Ptolemaic period. The Persians only briefly recaptured Egypt before being conquered by Alexander the Great. After Alexander died, his successors battled for control of his empire. Ptolemy I had been Alexander's governor of Egypt, and fled there (with Alexander's corpse) to become the new, independent ruler of Egypt. He conquered Judea by first infiltrating Jerusalem under the guise of performing sacrifices on the Sabbath and attacking/seizing power from the inside before subduing the surrounding region by force and enslaving a large number of POWs.

From then, Judea was conquered by the Seleucids in 200 BC, rebelled and gained independence in 141 BC, and held the status quo until the Romans arrived. As the Romans subjugated Judea before annexing Egypt, and then abolished the Jewish-governed province in 70 AD, there wasn't another time for an independent power from Egypt to invade a Jewish power in the southern Levant until the modern wars between Egypt and Israel.