Can HTTP GET have body?

Of course it can. But you shouldn’t use it. Some major products make use of GET’s body (f.i. Elastic). Still, it goes against RFC 7231 and could break caching and proxying.

Now, let's implement it. Using ASP.NET Core MVC it is straight forward:

using Microsoft.AspNetCore.Mvc;

namespace GetWithBody.Controllers;

[ApiController]
[Route("[controller]")]
public class GetWithBodyController : ControllerBase
{
    public record SomeThing(string Some, string Thing);
    [HttpGet]
    public IActionResult Token([FromBody]SomeThing? data)
    {
        if (data is null) return BadRequest();
 
        return Ok($"we received {data.Some} and {data.Thing}!");
    }
}

And the same goes to DELETE

[HttpDelete]
public IActionResult SomeOtherThing([FromBody] SomeThing? data)
{
    if (data is null) return BadRequest();

    return Ok($"we aiming to delete {data.Some} and {data.Thing}!");
}

References:

Empty Search | Elasticsearch: The Definitive Guide [2.x] | Elastic

RFC 7231 - Hypertext Transfer Protocol (HTTP/1.1): Semantics and Content

HTTP GET with request body

HTTP GET with Request body - Guidelines

Is an entity body allowed for an HTTP DELETE request?