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This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The main feature of obtained solutions <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>u</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mspace width="3.33333pt"></mspace><mi>v</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></mrow></semantics></math></inline-formula> is that the solution <inline-formula><math display="inline"><semantics><mrow><mi>u</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> is positive, and the other solution <inline-formula><math display="inline"><semantics><mrow><mi>v</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> may change sign. Finally, two examples with continuous function <inline-formula><math display="inline"><semantics><msub><mi>f</mi><mn>1</mn></msub></semantics></math></inline-formula> being positive and <inline-formula><math display="inline"><semantics><msub><mi>f</mi><mn>2</mn></msub></semantics></math></inline-formula> being semipositone are worked out to illustrate the main results.