You may build on your own property, but first check local zoning and building ordinances and codes to see whether there is a set-off requirement between the fences. You may be required to obtain a permit and there may be height restrictions and restrictions about the materials used, etc. Also, neighborhood associations sometimes have rules about fences, so if you belong to an association you will want to check that also. Also - be sure to call call to confirm the location of local utilities before you dig as you could be injured or liable for injuries caused from severing a power line, propane line, water line, etc.
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