Lets say I want to call out CQ on 145.340, 145.940, and 146.140 at the same time, am I allowed to call simultaneously on all three then monitor all three for replies?
A relevant rule your license requires is:
Each station licensee and each control operator must cooperate in selecting transmitting channels and in making the most effective use of the amateur service frequencies. (FCC Part 97.101(b))
While spamming multiple channels with the same transmission will save you time, it clearly isn't the most effective use of the bandwidth you're sharing with others. Further you can only respond to one at a time, so if you receive contacts on two of those channels, you'll essentially be ignoring a response to your question while you handle the other one.
It's not good use of the bandwidth, it could be considered selfish and annoying to other operators, and may be in violation of your license.
It appears that the simple legal answer is YES, BUT.
Transmitting on multiple frequencies is not illegal.
You mentioned both 146.340 and 146.940, and those require some care: If you are on 146.94 that is often a repeater output which would have an input on 146.34 - so even if you can hear people there, it is less likely that they would hear you on that frequency. To work people on .94 if there is a repeater you will have much greater success transmitting on .34
This also means that you would be interfering with the repeater and your own input signal if you transmitted on both .34 and .94 - so that isn't a good idea at all.
Plus, when working through repeaters keep in mind that many will want a CTCSS subaudible tone to unlock their squelch. This often indicates a closed repeater, say for specific club use as opposed to being open to passing tourists.
If you transmit without the tone you will likely interfere with an authorized user. That is a definite NO.
Also, you would transmit a QRZ (pronounced cue-are-zed) instead of a CQ on an FM frequency
If you do transmit on more than one frequency at a time, hopefully it is because you have the capability of answering any callbacks on any one of them. Otherwise it would only add to congestion without any benefit to you.
So that part is technically legal.