This can be accomplished using a custom model binder:
public class FormDataJsonBinder : IModelBinder
{
    public Task BindModelAsync(ModelBindingContext bindingContext)
    {
        if(bindingContext == null) throw new ArgumentNullException(nameof(bindingContext));
        // Fetch the value of the argument by name and set it to the model state
        string fieldName = bindingContext.FieldName;
        var valueProviderResult = bindingContext.ValueProvider.GetValue(fieldName);
        if(valueProviderResult == ValueProviderResult.None) return Task.CompletedTask;
        else bindingContext.ModelState.SetModelValue(fieldName, valueProviderResult);
        // Do nothing if the value is null or empty
        string value = valueProviderResult.FirstValue;
        if(string.IsNullOrEmpty(value)) return Task.CompletedTask;
        try
        {
            // Deserialize the provided value and set the binding result
            object result = JsonConvert.DeserializeObject(value, bindingContext.ModelType);
            bindingContext.Result = ModelBindingResult.Success(result);
        }
        catch(JsonException)
        {
            bindingContext.Result = ModelBindingResult.Failed();
        }
        return Task.CompletedTask;
    }
}
You can then use the ModelBinder attribute in your DTO class to indicate that this binder should be used to bind the MyJson property:
public class Dto
{
    public IFormFile MyFile {get;set;}
    [ModelBinder(BinderType = typeof(FormDataJsonBinder))]
    public MyJson MyJson {get;set;}
}
Note that you also need to serialize your JSON data from correctly in the client:
const formData = new FormData();
formData.append(`myFile`, file);
formData.append('myJson', JSON.stringify(obj));
The above code will work, but you can also go a step further and define a custom attribute and a custom IModelBinderProvider so you don't need to use the more verbose ModelBinder attribute each time you want to do this. Note that I have re-used the existing [FromForm] attribute for this, but you could also define your own attribute to use instead.
public class FormDataJsonBinderProvider : IModelBinderProvider
{
    public IModelBinder GetBinder(ModelBinderProviderContext context)
    {
        if(context == null) throw new ArgumentNullException(nameof(context));
        // Do not use this provider for binding simple values
        if(!context.Metadata.IsComplexType) return null;
        // Do not use this provider if the binding target is not a property
        var propName = context.Metadata.PropertyName;
        var propInfo = context.Metadata.ContainerType?.GetProperty(propName);
        if(propName == null || propInfo == null) return null;
        // Do not use this provider if the target property type implements IFormFile
        if(propInfo.PropertyType.IsAssignableFrom(typeof(IFormFile))) return null;
        // Do not use this provider if this property does not have the FromForm attribute
        if(!propInfo.GetCustomAttributes(typeof(FromForm), false).Any()) return null;
        // All criteria met; use the FormDataJsonBinder
        return new FormDataJsonBinder();
    }
}
You will need to add this model binder provider to your startup config before it will be picked up:
services.AddMvc(options =>
{
    // add custom model binders to beginning of collection
    options.ModelBinderProviders.Insert(0, new FormDataJsonBinderProvider())
});
Then your DTO can be a bit simpler:
public class Dto
{
    public IFormFile MyFile {get;set;}
    [FromForm]
    public MyJson MyJson {get;set;}
}
You can read more about custom model binding in the ASP.NET Core documentation: https://learn.microsoft.com/en-us/aspnet/core/mvc/advanced/custom-model-binding