You can add nodes to a node pool programmatically via the DigitalOcean API. For example, you can list the node pools in your cluster by sending a GET request to https://api.digitalocean.com/v2/kubernetes/clusters/<k8s-cluster-id>/node_pools. Using cURL it would look like:

$ curl -X GET -H "Content-Type: application/json" \
  -H "Authorization: Bearer $DO_TOKEN" \
  "https://api.digitalocean.com/v2/kubernetes/clusters/c801fb70-7086-4686-b4f0-95788435d032/node_pools" \
  | jq .

{
  "node_pools": [
    {
      "id": "c6561251-78c7-4824-830e-92610d1d7e5e",
      "name": "example-cluster-01-default-pool",
      "size": "s-1vcpu-2gb",
      "count": 3,
      "tags": [
        "k8s",
        "k8s:c801fb70-7086-4686-b4f0-95788435d032",
        "k8s:worker"
      ],
      "nodes": [
        {
          "id": "8d077fb6-8350-4564-936d-cfca4ceab9ee",
          "name": "example-cluster-01-default-pool-yqdj",
          "status": {
            "state": "running"
          },
          "created_at": "2019-05-21T15:22:36Z",
          "updated_at": "2019-05-21T15:26:02Z"
        },
        {
          "id": "a35e9b2b-d0d5-4790-976f-0ceba17479e9",
          "name": "example-cluster-01-default-pool-yqdr",
          "status": {
            "state": "running"
          },
          "created_at": "2019-05-21T15:22:36Z",
          "updated_at": "2019-05-21T15:26:02Z"
        },
        {
          "id": "cc32b6b5-5a05-49b1-b12e-8adb971ef3c9",
          "name": "example-cluster-01-default-pool-yqdb",
          "status": {
            "state": "running"
          },
          "created_at": "2019-05-21T15:22:36Z",
          "updated_at": "2019-05-21T15:26:02Z"
        }
      ]
    }
  ]
}

Now that we have the ID for the node pool, we can send a PUT request to https://api.digitalocean.com/v2/kubernetes/clusters/<k8s-cluster-id>/node_pools/<node-pool-id> adding an additional node:

$ curl -X PUT -H "Content-Type: application/json" \
  -H "Authorization: Bearer $DO_TOKEN" \
  -d '{"name": "example-cluster-01-default-pool-yqdj","count": 4}' \
  "https://api.digitalocean.com/v2/kubernetes/clusters/c801fb70-7086-4686-b4f0-95788435d032/node_pools/c6561251-78c7-4824-830e-92610d1d7e5e" \
  | jq .

You can remove nodes using the same technique or delete a specific node if you want finer control.