Mishnah Parah 7:3: One who sanctifies [the water] with one hand and does work with one hand, if [the work is] for himself, it is invalid; and if it is for another, it is valid. One who sanctifies for himself and for another, his is invalid and the other's is valid. One who sanctifies for two [others] at once, both are valid.

הַמְקַדֵּשׁ בְּאַחַת יָדוֹ וְעוֹשֶׂה מְלָאכָה בְאַחַת יָדוֹ, אִם לוֹ, פָּסוּל. וְאִם לְאַחֵר, כָּשֵׁר. הַמְקַדֵּשׁ לוֹ וּלְאַחֵר, שֶׁלּוֹ פָּסוּל, וְשֶׁל אַחֵר כָּשֵׁר. הַמְקַדֵּשׁ לִשְׁנַיִם כְּאֶחָד, שְׁנֵיהֶן כְּשֵׁרִין:

Mishnah Parah 7:4: [One who says to his fellow,] "Sanctify for me and I will sanctify for you," the first [one sanctified] is valid. "Fill for me and I will fill for you," the latter [one filled] is valid. Sanctify for me and I will fill for you," both are valid. "Fill for me and I will sanctify for you," both are invalid.

קַדֵּשׁ לִי וַאֲקַדֵּשׁ לָךְ, הָרִאשׁוֹן כָּשֵׁר. מַלֵּא לִי וַאֲמַלֵּא לָךְ, הָאַחֲרוֹן כָּשֵׁר. קַדֵּשׁ לִי וַאֲמַלֵּא לָךְ, שְׁנֵיהֶם כְּשֵׁרִים. מַלֵּא לִי וַאֲקַדֵּשׁ לָךְ, שְׁנֵיהֶם פְּסוּלִים: