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If I have recorded a common law lien against my property and then record a Satisfaction of Lien...

If I have recorded a common law lien against my property and then record a Satisfaction of Lien so that I can transfer the property into a Pure Trust Organization - or anywhere else - can I then reinstitute the common law lien and again record it with the County Recorder?

No.  Once you have recorded a notice of Satisfaction of Lien, then the lien has been satisfied!  You cannot “reactivate” it, because it no longer exists. However, if you establish a new claim against the property then you can record a new common law lien.