要实现Webview下载其他格式的文件，需要设置Webview的DownloadListener，同时在Manifest文件中添加写入存储权限。

以下是示例代码：

1. 向Webview设置DownloadListener

public class MainActivity extends AppCompatActivity {

private WebView webView;

@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);
    webView = findViewById(R.id.web_view);
    webView.setWebViewClient(new WebViewClient());
    webView.getSettings().setJavaScriptEnabled(true);

    // 设置DownloadListener
    webView.setDownloadListener(new DownloadListener() {
        @Override
        public void onDownloadStart(String url, String userAgent, String contentDisposition, String mimetype, long contentLength) {
            // 下载文件
            downloadFile(url, contentDisposition, mimetype);
        }
    });

    webView.loadUrl("http://example.com/file.pdf");
}

// 下载文件
private void downloadFile(String url, String contentDisposition, String mimetype) {
    DownloadManager.Request request = new DownloadManager.Request(Uri.parse(url));
    request.setTitle(contentDisposition);
    request.setMimeType(mimetype);
    request.setDestinationInExternalPublicDir(Environment.DIRECTORY_DOWNLOADS, "file.pdf");

    // 获取DownloadManager
    DownloadManager downloadManager = (DownloadManager) getSystemService(DOWNLOAD_SERVICE);
    downloadManager.enqueue(request);
}

}

2. 在Manifest文件中添加写入存储权限