At the end of Numbers 15 we find familiar words from the third paragraph of the Shema: "... so that you do not follow your heart and eyes in your lustful urge." The reference is to seeing the tzitzit on clothing or a tallit, and remembering the commandments, and thereby reigning in inappropriate appetites.
To which the Babylonian Talmud responds, "From this Rabbi said, 'Let a man not drink from one cup and cast his eye on another.'" He wasn't discussing cups. The Talmud says, "Even if they are both his wives."
The source of the prohibition of satisfying two urges simultaneously comes from the use of the word "levav," meaning heart, but spelled with two letters "beit." It can also be spelled with one letter "beit." The Rabbis say that the heart is the source of desire, and therefore prohibits pursuit of two desires simultaneously.
A different direction is famously cited in Berachot 54a, regarding the Shema. There is says to seek God with both inclinations, your good inclination and your evil inclination. Employ both in the love of God. Rather than prohibiting satisfying the lust for two things simultaneously, urging us to focus on just the one, this interpretation is that in fulfilling God's commandments we should employ both our good inclination and our evil inclination. But how do we do that?
The trick is first to forthrightly identify the evil inclination. You may be doing the right thing for the wrong reason. You may be giving tzedakah to look good in other people's eyes. You may be honoring your parents out of guilt, or complimenting a child for your own benefit. But, it turns out, even in the evil inclination can be turned to benefit, to spirituality and to moral improvement.
Exodus 23:5 teaches us to identify our evil inclination, and then to do the opposite of our impulse, not to benefit someone else but to train our own souls. There the instance is helping your enemy, the person you'd least like to help out. It's more important to help that person than even a friend, because it trains us to be kind to all creatures. When we identify the evil inclination in ourselves, which all of us possess, we can work to correct it, and thus root out negative emotions. Thus, both inclinations can be used to do the right thing: the good and the evil inclination.
So what happens when you have two things you desire? How about saying to ourselves, "Thank you God for creating pleasures in my life. Thank you God for keeping me alive. Thank you for more than one source of satisfaction in my life. And thank you, God, for allowing me to control my urges, such that I can change the animal nature in me to live on a higher plane, as you would have me live. Thank you for the ability to discern right from wrong, and the willingness to train my soul to be holy."