Yes, a student can have a 504 plan and an IEP.
For example, a student with an IEP comes to school needing a temporary medical plan, should receive a 504 plan. This would be a short term 504 plan for short term accommodations. A broken hand would require a student to have the accommodation of a scribe (someone to write for the student).
These instances are few and far, though.
In general, everything that is included in a 504 plan can be included in an IEP so there is not typically a need for both.
All 504 Academic Testing Academic Testing Reports Achievement Testing Reports Back To School B/d Reversals Coronavirus COVID-19 Discrepancy Model Distance Learning Distance Learning With LD ELL Executive Functioning Extended School Year First Year Special Education Teacher Advice FREEBIES Goal Tracking IEP IEP At A Glance IEP Goals IEP Meetings Learning Disability Oral Reading Fluency Positive Affirmations For Special Education Students Progress Monitoring Reading Remote Learning RTI Rubrics Running Records SEL For Learning Disabilities Special Ed Teacher Interview Questions Special Ed Teacher Job Description Special Education Special Education Progress Reports Special Education Reading Special Education Reading Programs Special Education Students Special Education Teachers Special Education Teachers Positive Affirmations Special Education Teacher Tips Special Education Websites Specially Designed Reading Instruction Teaching Strategy Wilson Reading Wilson Reading IEP Goals Writer's Workshop