Wait for tulips to complete their blooming and growing season. Allow the foliage to yellow and die back on its own, as the plant gathers sun, water and nutrition for the next year's bloom at this time. The best time for division and transplant is in fall, near the first frost of the year.
Prepare a new site for the additional tulip bulbs. Put the tulips in a spot that gets at least four to six hours of bright sun every day, with quick drainage and air circulation. Never plant tulips in areas that puddle. Allot 3 to 4 inches to each bulb you expect to dig.
Dig into the top 10 inches of soil in the site to prepare a deep, loose foundation for the new tulip bulbs. Dig 4 to 5 inches of organic compost or peat moss into the tilled soil for moisture retention and nutrition, and add bone meal or bulb fertilizer to the site per manufacturer directions.
Dig around the edges of your established tulip bed, to a depth of 8 inches. Use intact foliage to find as many bulbs as you can, and dig inwards with your hands to find bulbs without foliage. Pull all the bulbs from the soil.
Separate the tulip bulbs at natural divisions. Use a knife to cut bulbs that have these divisions, or move entire bulbs. Don't disturb roots or papery casings during this process. Move half the bulbs to the new site.
Mix bone meal or bulb fertilizer into the soil in the old plot to give the bulbs better nutrition in this site. Replant the bulbs in new and old beds, at more appropriate spacing. Place each bulb 8 inches deep, with the pointed ends up. Give each bulb 3 to 4 inches of growing space, and make sure that none of the bulbs touch underground.
Water each site until the soil is moist to a depth of 10 inches to establish the plantings, then spread 2 inches of mulch over the soil to protect the bulbs through winter.