Unlike in the world of publishing, simultaneous submissions are perfectly all right in grant proposals. In fact, in some cases, it's mandated or at least expected.

In some areas, the major funders meet regularly to discuss what part each wants to play in capital campaigns or major community initiatives. In this case, if you haven't submitted proposals to all the major funders, you risk offending one, or worse, being cut out of funding from all of them for lack of planning and communication.

It's also perfectly appropriate to submit portions of a project to various funders all at once or to submit a federal grant proposal at the same time that you are seeking local support. In fact, this too is often expected. You will have to seek funds to sustain a project over its first several years, so why not try to raise as much as you can to see it through the start-up? Funders are almost always more interested in new projects than they are in ongoing ones, which they come to see as “continuing operations.”