Let's go to a couple of Orthodox Jews and a couple of Orthodox Jewish rabbis to dispute the claims that the Triune Godhead is not a truly biblical Jewish teaching.
Our first Orthodox Jewish rabbi is Moses, who teaches us about the Complex Unity of God in Genesis 19. The context is of YHWH coming to earth and speaking - and even dining with - Abram just before He destroys the evil cities of Sodom and Gomorra:
24 Then the LORD caused to rain upon Sodom and upon Gomorrah brimstone and fire from the LORD out of heaven;
Transliterated, it would read thus:
24 Then YHWH caused to rain upon Sodom and upon Gomorrah brimstone and fire from YHWH out of heaven;
Our second teacher is an Orthodox Jew, King Solomon:
ד מִי עָלָה-שָׁמַיִם וַיֵּרַד,
מִי אָסַף-רוּחַ בְּחָפְנָיו מִי צָרַר-מַיִם בַּשִּׂמְלָה--
מִי, הֵקִים כָּל-אַפְסֵי-אָרֶץ:
מַה-שְּׁמוֹ וּמַה-שֶּׁם-בְּנוֹ, כִּי תֵדָע. (Hebrew)
4 Who hath ascended up into heaven, and descended? Who hath gathered the wind in his fists? Who hath bound the waters in his garment? Who hath established all the ends of the earth? What is his name, and what is his son's name, if thou knowest?
Again, the text above is from the Jewish Publication Society's Mechon-Mamre Bible. You can see both passages for yourself here:
Our third tutor is the Orthodox Jew King David, who also shows us that God is a complex unity in Psalm 2:
11 Serve the Lord with reverential awe and rejoice with trembling.
12 Pay homage to the Son or He will be angry and you will perish in your rebellion, for His anger may ignite at any moment. All those who take refuge in Him are happy.
Next we turn to a Jewish prophet, the prophet Isaiah, who said in Isaiah 9:6...
Our final Source is the most famous of them all by far. He is the best known Jew in the whole world and has been talked about for the last 2,000 years and will be talked about all through eternity.
I'm referring to the world-renowned Orthodox Jewish rabbi who Christians call Yeshua ha Mashiach, or to us English speakers, Jesus the Messiah. Yeshua the Orthodox Jewish Rabbi delineates the triune nature of the Biblical Godhead for us when He says in Matthew 28:
19 "Go, therefore, and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit..."
Yeshua the Jewish Rabbi teaches us that God has One name, but that His name is shared by the Father, the Son and the Holy Spirit. Further study of the Bible shows that the 3 Persons in the one God are co-equal, co-eternal and co-existent.
More information is available here:
Answering Your Toughest Questions, Episode 10, The Trinity. God is One, Not Three: Dr. Michael Brown
Answering Your Toughest Questions, Episode 11, The Deity of the Messiah: Dr. Michael Brown
The Jewish Trinity: Dr Michael Heiser
The Biblical Basis for the Doctrine of the Trinity
The Lord Our God is One!