Yes you could.
First, you have to know which module you want to retrieve it's content. This is usually by querying a tab to get module list. Then based on your module list, you can choose which module you want to retrieve it's content. I will show you an example, notes that this is only proof of concept that i've been doing for my client. Feel free to modify.
Suppose that you have Home page. Then in that page you have one module (let say Events module with it's contents).
Open your Visual Studio, and create your custom module. Feel free to name it. Add one web user control with simple name like View.ascx or something. Go to View.ascx.cs (your code behind) then add this code in your Page_Load method.
TabController tc = new TabController();
// Home is your other tab on which you want to load tab's modules
// in reality, you can make it as dropdownlist to show all user's tab and make a choice
TabInfo ti = tc.GetTabByName("Home", PortalSettings.PortalId);
// Show tab's module from Home page
ModuleController mc = new ModuleController();
Dictionary<int, ModuleInfo> listModules = mc.GetTabModules(ti.TabID);
string ctrl = "";
foreach (KeyValuePair<int, ModuleInfo> item in listModules) {
ModuleInfo mi = item.Value;
ModuleInfo eventModule = mc.GetModule(mi.ModuleID, ti.TabID);
// Notes that this is because you have only one module
// in reality, you can make it as dropdownlist
// so user can choose which module they want to load
ctrl = mi.ControlSrc;
}
PortalModuleBase objPMB = (PortalModuleBase)this.LoadControl("~/" + ctrl);
objPMB.ModuleConfiguration = this.ModuleConfiguration;
objPMB.ID = System.IO.Path.GetFileNameWithoutExtension(ctrl);
// Create placeholder control dynamically to inject portalmodulebase
PlaceHolder ph = new PlaceHolder();
ph.Controls.Add(objPMB);
this.Controls.Add(ph);
Build your custom module. And install it into your DNN website. Let's go to the next step.
You create another page with name Page2 and drop your custom module onto it. Then you will see that your custom module will render as Event module from Home page or we can say that you have been embedding your Events module inside another module. :)
HTH.