Texas Civil Practice and Remedies Code - CIV PRAC & REM § 34.072. Timing of Execution and Return

(a) An officer receiving a writ of execution may return the writ after the first levy, or attempted levy, if the judgment creditor cannot designate any more executable property currently owned by the judgment debtor at the time of the first levy or first attempted levy.

(b) Notwithstanding Rule 637, Texas Rules of Civil Procedure, an attempt to levy on property may begin any time during the life of the writ, provided that the officer shall allow enough time for completing the sale of the property.