YES, , but, the catch is - the code logic you have in mind can't be created with online button generator. As the owner of the recepient account, you would like to know where the money should go if you are supporting multiple groups.
The online button generator is a great tool and works well for most people however, it's intended for straight forward simple donations - when you need choices, multiple input and anything outside the box, then the code has to be manually created. Note, when code is created manually, it's not stored on the PayPal servers - it gets pasted into your web page - if your web page supports HTML forms (which is what the PayPal button code is), then you're good to go. If your web page requires text or URL links, then you are limited as to what you can create - meaning, you can't offer choices, text input boxes, etc.
Here's a basic manually created donation example that allows your donors to make a choice of where the money is to go and there's also an optional text input box. The details are passed on to the PayPal Checkout Screens and to you so you know what the funds are intended for.
Wag your tail, custom coding is Fun !!!
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<html>
<head>
<title></title>
</head>
<body>
<!-- Start of Form -->
<form target="_self" action="https://www.paypal.com/cgi-bin/webscr" method="post">
<input type="hidden" name="cmd" value="_donations">
<!-- Replace "business" value with your PayPal Email Address or your Merchant Account ID -->
<input type="hidden" name="business" value="your email address">
<input type="hidden" name="no_shipping" value="1">
Choose Your Organization:
<select name="item_name">
<option value="Good Will" selected>Good Will</option>
<option value="United Way">United Way</option>
<option value="Boys and Girls Club">Boys and Girls Club</option>
<option value="West Side Shelter">West Side Shelter</option>
<option value="Pets and Vets">Pets and Vets</option>
</select>
<br><br>
<!-- Start Optional Text Input -->
<input type="hidden" name="on0" value="In Memory Of">In Memory of - Enter Name:
<input type="text" name="os0">
<!-- End Optional Text Input -->
<br><br>
<input type="hidden" name="no_note" value="1">
<input type="hidden" name="currency_code" value="USD">
<!-- Start Tax Override meaning No Tax -->
<input type="hidden" name="tax" value="0">
<!-- End Tax Override -->
<!-- <input type="hidden" name="bn" value="PP-DonationsBF"> -->
<input type="image" src="https://www.paypal.com/en_US/i/btn/x-click-but21.gif" border="0" name="submit" alt="Make payments with PayPal - it's fast, free and secure!">
<img alt="" border="0" src="https://www.paypal.com/en_US/i/scr/pixel.gif" width="1" height="1">
</form>
<!-- End of Form -->
</body>
</html>
