Sure!

```
from flask import Flask, request

app = Flask(__name__)

@app.route('/', methods=['POST'])
def encrypt():
    request_body = request.get_json(force=True)
    input_str = request_body['input']
    shift = request_body.get('shift', 1)  # default shift is 1 if not specified

    output_str = ''
    for char in input_str:
        if char.isalpha():
            char_code = ord(char)
            if char.isupper():
                base = ord('A')
            else:
                base = ord('a')
            char_code = (char_code - base + shift) % 26 + base
            char = chr(char_code)
        output_str += char

    return output_str

app.run(port=3000)
```

This modified application also takes an optional shift parameter in the request body, which specifies the number of characters to shift by in the Caesar cipher. If the shift parameter is not specified, it defaults to 1.

You can test this modified application with curl as:
```
curl -X POST -H 'Content-Type: application/json' -d '{"input": "Hello server", "shift": 5}' http://127.0.0.1:3000/
```
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