The Austro-Hungarian Empire was home to eleven major ethno-language groups: Germans, Hungarians, Polish, Czech, Ukrainian, Slovak, Slovene, Croatians, Serbs, Italians and Romanians.
IN 1867 the Hapsburgs formed a dual monarchy with Hungary. In the years between 1880 and 1918 there was talk of "promoting" Croatia as a third partner in the Empire (movement often called Trialism). The end of WWI kinda made this vision moot.
In my admittedly limited knowledge I have not heard of a discussing to elevate the Czechs to the status that Hungary and Croatia (potentially) enjoyed. Why was that? They seemed to have 'all the right stuff' to be a co-equal partner in the Empire. Why where they left out when two over internal states were given prominent near co-equal positions?
The main problem was a big German minority in Bohemia and Moravia.
The nationality was decided by “Obcovací řeč” (Umgangssprache), the language which the person claimed that he used in his community. This criterion probably overestimated the number of Germans. According to the census in 1910 6 291 237 persons stated Czech language, 4 241 918 in Bohemia, 1 868 971 in Moravia and 180 348 in Silesia. German language stated 3 512 682 persons, 2 467 724 in Bohemia, 719 435 in Moravia and 325 523 in Silesia. It was 62,9 % Czech, 34,6 % Germans and 1,6 % of other nationalities.
At the end of the 18th century Czech was only a language of the common people and declining. Thanks to the Czech National Revival and the efforts of many people Czech nation was established as a modern nation. In 1867, when Austria-Hungary was created, Czechs society was not so organized as Hungarian.
German was a more prestigious language. It was used in the central offices. For Czech intellectuals, employees of state and clerks it was necessary to know German. Even in the mostly or only Czech speaking areas. On the contrary, for Germans it was possible to make a career without knowing Czech.
Czech politics tried to equalize Czech language with German. After a period of passive resistance (1863-1878) the Czech politics started to support Austrian government of Eduard Taaffe in exchange for some concessions (“drobečková politika - “small crumbs politics”).
One of them was Stremayrova jazyková nařízení (Stremayr Ordinances) in 1880 in which the correspondence with authorities can be also in Czech, but internal communication stayed in German.
This tried to change prime minister Badeni in 1897 when he issued Badeni's language ordinances. By them Czech and German languages were equal. In practice it meant that German clerks had to learn Czech. It was totally unacceptable for them. After a big opposition of not only Germans from Bohemia and Moravia but also from Austria, the emperor Franz Josef I. dismissed Badeni and his language ordinances were annulled.
There was also another solution: to divide the territory into German and mixed parts which was unacceptable for Czech politics. So the situation reached a stalemate which was never resolved until the end of Austrian-Hungarian empire
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Michael Borovička, Jiří Kaše, Jan P. Kučera a Pavel Bělina (2013), Velké dějiny zemí Koruny české XII.a, XII.b