I would expect party rules to prohibit that, but you never know with the GOP.
You could only run in two Primaries and be on the Nov ballot if you won both. Lose one, and you are barred from being on the Nov ballot as a Primary loser.
Now. If Texas had a system like NY where the Conservative Party sometimes endorses the Republican candidate, that would work. A Conservative Party nominating by convention after the Primary could nominate another Party’s primary winner. Just not a loser.