How to handle multiple projects with a high-level of dependencies?

Certainly having explicit schedule dependencies linked together via MS Project is important to do, but I like to go one step further. For projects where there are significant dependencies (i.e. where one project could create a schedule slip in another) I like to maintain a cross-project dependency grid where a project manager lists out those projects that have some type of dependency, who the project manager is, and how the projects can hurt each other. The PM then uses this in a brief periodic checkpoint with the other project managers to discuss the dependencies and assess the likelihood in which the projects can hurt each other. Doing so helps give advanced warnings on dependent schedule slips and mitigate them before they actually occur.

@Rachel

Maybe you type the wrong value in the ID cell. For more detail, I will show you a quick way to do that.

Assuming that you have a Master project with two sub-projects "Project 1" and "Project 2". When you open Master project you will see the table as bellow (You may need to add ID column to show ID of task):

ID TaskName Predecessors
1 Project 1
1 Project 1 Task 1
2 Project 1 Task 2
2 Project 2
1 Project 2 Task 1
2 Project 2 Task 2

In the Predecessor cell of the task "Project 2 Task 1" you can type "Project 1\1" without quotation marks to link "Project 2 Task 1" and "Project 1 Task 1"

Hi Rachel!
In your question you asked for any solution, not limited by MS Project capabilities.
Spider Project Professional does it easily.
You just need to create a portfolio, select projects that will be included in this portfolio, open portfolio model that looks like one large project where included projects look like subprojects, add links between activities of different projects, calculate portfolio schedule and then distribute portfolio projects.
Now all projects will remember their external links and at any moment you can consolidate the portfolio and recalculate portfolio schedule.
Each project remember the portfolio where it belongs and there is an option to calculate project schedule taking into account portfolio constraints.
Portfolio schedule is created taking into account not only activity dependencies but also resource and financial constraints.
Let me know if you will have any questions.