can novelists submit to more than one publisher?

I'm just wondering because I was considering submitting novels and short stories to Mockingbird Lane Press, as sort of a launching pad to jumpstart my career as a novelist; however, because this is such a small-time publisher with somewhat strict guidelines, (for instance scenes consisting of graphic erotica are not acceptable) I was also considering submitting my works to larger publishers that will be more accepting of my medium of writing. (Although I have some rapport with the company's sister magazine "The Storyteller", I usually have been able to send only stories that consist of mostly PG-rated themes, and I hope to submit stuff that have heavier themes that touch on abuse some including sexually graphic themes such as molestation, rape, and other intense situations that I know Mockingbird Lane Press does not accept. I don't know if one would need to be familiar with Mockingbird's submission guidelines in order to know the answer to my question but I hope someone knows something, thanks in advance.