Answer: Bulbs are storage organs and need the foliage to remain until it dies back naturally so the leaves can transport carbohydrates back into the bulbs, but you can certainly cut off the spent flowers. You should be able to plant around or near your existing bulbs without problem. To have something in bloom almost all year around, consider planting peonies, iris and daylilies, phlox, asters and violets in your garden, then add some annuals (which you can change out as the seasons change).
Best wishes with your garden!
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