The following Talmud passage (Taanit 8b) indicates we must not pray for too many things:
In the days of Rabbi Shmuel bar Nahmani there was a famine and a deadly plague.
People asked: “What shall we do? Shall we pray for [the removal] of both? That is not possible. [We do not pray for two things at a time.] Let us then pray for [the removal of] the plague and we will endure the famine.”
Thereupon Rabbi Shmuel bar Nahmani said to them: “Let us rather pray [for the removal of] the famine, because when the All-Merciful gives plenty, He gives it for the living, [not for the dead,] as it is said [in the Book of Psalms]: “You open Your hand and give to each living thing according to his need”.” [Ps. 145:16]
How how do we know that we do not pray for two things [at the same time]?
Because it is written [in Ezra]: So we fasted and petitioned our God concerning “this” [in the singular]. [Ezra 8:23] This indicates that there were other things for which they could have prayed [but didn’t].
In the Land of Israel, it was reported in the name of Rabbi Haggai that it could [also] be deduced from this verse [in Daniel]: … Implore the God of Heaven for help concerning “this” mystery [in the singular]. [Dan. 2:18] This implies that there were other things for which they could have prayed [but didn’t].
Is this halacha or a suggestion? We pray for many things at the same time all the time. The daily Amidah has 13 petitionary prayers. If you say: It's not at the same time; one follows another, then I ask: What is 'At the same time'?