You can have several signatures on the same form, with the last one 'locking' everything - so that's not a problem. If the form is a legal document it's the signatures themselves which are the issue.
You cannot use digital signatures if one of the parties is a random client, as they won't have their own ID. Anyone can create a self-signed ID but they're legally invalid, so they would have to buy a commercial one. That can take several days to arrive and costs a lot of money as the issuer must verify the customer's identity beyond question (they'll ask for passports, etc.).
Digital IDs need unlocking each time they're used (e.g. a password or a cipher dongle) - so sharing the computer between several workers isn't that much of a risk, though it's considered very bad practice to allow anyone else access to a private key file that uses password encryption as they could brute-force it given enough time. Normally you carry your IDs on a USB drive.
The 'ink' signatures where you just draw with your mouse/stylus are not legally-binding either, as the fidelity of the image is too low - anyone could scrawl a copy of your signature and even you wouldn't be able to tell the difference.
If the form isn't important you could allow the client to 'ink' sign the file, then your form-owner applies a digital ID signature in a second field, locking the entire form, but it still doesn't make the first signature legal as there's no verifiable witness. Adobe's solution to allow a random person or list of people to sign something is to post the form to EchoSign, where Adobe acts as the witness, but that's an online process - it happens through email and couldn't be done in a meeting with a shared computer.
When using the EchoSign app for iOs, in person signing is an option as well.
Amiga2k0 have a look at the Echosign product it will do what you need.