Typescript：是否将联合类型传递给重载函数

我有这样一门课:

type Params = {
    data: string | string[]
}

class Test {
    data: string | string[]

    constructor(params: Params) {
        this.data = this.initData(params.data)
    }

    initData(data: string): string
    initData(data: string[]): string[]
    initData(data: string | string[]): string | string[] {
        if (typeof data === 'string') {
            return data as string
        } else {
            return data as string[]
        }
    }
}

但我得到了这样的错误:

No overload matches this call.
  Overload 1 of 2, '(data: string): string', gave the following error.
    Argument of type 'string | string[]' is not assignable to parameter of type 'string'.
      Type 'string[]' is not assignable to type 'string'.
  Overload 2 of 2, '(data: string[]): string[]', gave the following error.
    Argument of type 'string | string[]' is not assignable to parameter of type 'string[]'.
      Type 'string' is not assignable to type 'string[]'.ts(2769)

Untitled-1(38, 5): The call would have succeeded against this implementation, but implementation signatures of overloads are not externally visible.

我发现了一个愚蠢的变通办法，它有帮助:

constructor(params: Params) {
    this.data = this.initData(params.data)

    if (typeof params.data === 'string') {
        this.data = this.initData(params.data)
    }
    else {
        this.data = this.initData(params.data)
    }
}

我有点明白为什么这是可行的，但也许有更好的方法来解决这个问题？