Short answer. No. Section 4 of Rule 43 says only one motion for reconsideration shall be allowed. The fifteen-day appeal period runs from the denial of that single motion, duly filed in accordance with the governing law of the agency, so a second motion does not extend or restart your time to appeal.
What the law says
Only one motion for reconsideration shall be allowed.
Rule 43, Section 4 — Period of appeal. Read the full provision →
What the law says
The appeal shall be taken within fifteen days from notice of the award, judgment, final order or resolution, or from the date of its last publication, if publication is required by law for its effectivity, or of the denial of petitioner's motion for new trial or reconsideration duly filed in accordance with the governing law of the court or agency a quo.
Rule 43, Section 4 — Period of appeal. Read the full provision →
The one-motion rule, stated without qualification
Section 4 answers your question in four plain words: Only one motion for reconsideration shall be allowed. The rule does not distinguish between different agencies or different kinds of rulings — it sets a single limit that applies across the board to matters governed by this section on the period of appeal, whatever agency issued the award, judgment, final order, or resolution you are contesting.
Where the fifteen-day appeal period comes from
Section 4 ties your appeal deadline to that one motion: The appeal shall be taken within fifteen days from notice of the award, judgment, final order or resolution, or from the date of its last publication, if publication is required by law for its effectivity, or of the denial of petitioner's motion for new trial or reconsideration duly filed in accordance with the governing law of the court or agency a quo. The countdown starts from the denial of that single, duly filed motion, not from whatever second motion you might attempt afterward.
Why filing a second motion does not help your timeline
Because Section 4 allows only one motion for reconsideration, a second motion is not one the rule recognizes as duly filed for purposes of restarting the fifteen-day period. Your appeal clock keeps running from the denial of the first motion regardless of whether you file another one, which is why relying on a second motion to buy more time is risky under this section.
What to do instead if you need more time
Section 4 does provide a separate, narrow avenue for extra time: upon proper motion and full payment of the docket fee before the reglementary period expires, the Court of Appeals may grant one additional period of fifteen days to file the petition for review, and any further extension is granted only for the most compelling reason and never beyond fifteen days. That route runs through the Court of Appeals, not through additional motions at the agency level.