There are at least the following 4 possibilities showing up on Lancs On Line Parish Clerks site (a free site for Lancs Parish Records).
Baptism: 20 Aug 1775 St Peter and St Paul, Ormskirk, Lancashire, England
James Beesley - Son of James Beesley & Catharine
Abode: Lath[om]
Register: Baptisms 1771 - 1794, Page 19, Entry 31
Source: LDS Film 1849663
Baptism: 11 Jan 1778 St Peter and St Paul, Ormskirk, Lancashire, England
William Beesley - Son of James Beesley & Catharine
Abode: Orms[kirk]
Register: Baptisms 1771 - 1794, Page 30, Entry 33
Source: LDS Film 1849663
Baptism: 9 Feb 1781 St Peter and St Paul, Ormskirk, Lancashire, England
Jno Beesley - Son of Jas Beesley & Catharine
Abode: Orms[kirk]
Register: Baptisms 1771 - 1794, Page 45, Entry 18
Source: LDS Film 1849663
Baptism: 15 Apr 1785 St Peter and St Paul, Ormskirk, Lancashire, England
Michael Beesley - Son of James Beesley & Catharine
Abode: Orms[kirk]
Register: Baptisms 1771 - 1794, Page 66, Entry 21
Source: LDS Film 1849663
You would think there would be others actually and there may well be!