OK, which two protestant denominations believe the same and cooperate as the sui iuris Catholic Churches do? Followup: if they do aren’t they already the same denomination? If not, why not?
The following churches are identical in their theological beliefs and share full pulpit and altar fellowship. That is, they cooperate with each other fully - even to the point of exchanging clergy, just as your various sui juris churches technically can (although few do).
Evangelical Lutheran Church of Ghana (ELCG)
Evangelical Lutheran Church in Kenya (ELCK)
Evangelical Lutheran Church of Liberia (ELCL)
The Lutheran Church of Nigeria (LCN)
Free Evangelical - Lutheran Synod in South Africa (FELSISA)
Lutheran Church in Southern Africa (LCSA)
Eglise Luthérienne du Togo (ELT)
China Evangelical Lutheran Church (CELC)
The Lutheran Church - Hong Kong Synod (LCHKS)
India Evangelical Lutheran Church (IELC)
Japan Lutheran Church
Lutheran Church in Korea (LCK)
Gutnius* Lutheran Church (GLC)
The Lutheran Church in the Philippines (LCP)
Lanka Lutheran Church (LLC)
Evangelisch-Lutherse Kerk in België (ELKB)
Den evangelisk-lutherske Frikirke i Danmark (ELFD)
The Evangelical Lutheran Church of England (ELCE)
Église Évangélique Luthèrienne - Synode de France (EEL-SF)
Selbständige Evangelisch-Lutherische Kirche (SELK-Germany)
Evangelical Lutheran Church of Latvia (ELCL)
Consistory of the Evangelical Lutheran Church of Lithuania (CELCL)
The Lutheran Church in Norway
Igreja Evangélica Luterana Portuguesa
Evangelical Lutheran Church of Ingria in Russia (ELCIR)
Siberian Evangelical Lutheran Church (SELC)
Iglesia Evangélica Luterana Argentina (IELA)
Igreja Evangélica Luterana do Brasil (IELB)
Iglesia Luterana Confesional de Chile (ILC-CHILE)
Iglesia Luterana en Guatemala (ILG)
Sinodo Luterano de Mexico (SLM)
Iglesia Evangélica Luterana del Paraguay (IELP)
Iglesia Luterana de Venezuela (ILV)
Lutheran Church - Canada (LCC)
The American Association of Lutheran Churches (TAALC)
Eglise Evangelique Lutherienne D’Haiti (ELCH)
The Lutheran Church-Missouri Synod (LCMS)
But, depending on definitions, it may or may not be
entirely correct to say they are all the same denomination, as they do use slightly differing forms of church governance and/or particular liturgies. This is part of the reason the “35,000 Protestant splinter groups” argument is absurd. These 37 legally incorporated bodies are, effectively, identical and entirely fraternal.