The short answer is yes they can, but ordinarily they only attach one source of funds at a time unless there are other circumstances.
You will need to consult with a consumer protection or bankruptcy lawyer locally. Many lawyers on this site offer a free consultation and you might find one near you and make an appointment for specific legal counseling.
1. Start keeping a detailed log of all calls and letters and a paper file of all information. Because persistent violations of the FDPCA are punishable by statutory fines and attorney’s fees under federal law, but you need hard evidence.
2. Make a written demand that all further communications from creditors is in writing under 15 USC 1692 (c).
The letter should also contain a dispute of the validity of the charges and include a demand for a complete accounting with signatures, and all contents of their file.
The creditor then has 30 days to reply and they may not take any action until you have been sent the validation. Bear in mind that this may be motivation for the collector to work your account when the file comes to them from the original creditor with new information.
3. Do not give them any personal information because that is how collectors decide on which accounts to recommend suing. Remember they may not tell the truth and will say just about anything to get a payment from you and that payment reaffirms the debt, gives them information about you and your bank and ability to pay.
4. If you are going to make payments use money orders and not personal checks, wire transfers, money grams, or “check by phone” because if they find a bank account the collector will be more likely recommend a lawsuit the their legal department.
5. All collections are negotiable; the original creditor has given up and is losing up to 50% on the face value already either by splitting any return or selling at a huge discount. In addition, the costs of a lawsuit although discounted still are a factor in the decision to settle with you.
If you are going to settle mark the check “settled-in-full” at the very top back of the check and include a letter explaining you are offering a settlement, keep copies of everything.
6. Get written confirmation of any payment plan the agency will accept before making a payment.
7. Specify in writing that all payments will be applied to principle first.
If you are ready to throw in the towel go see a local bankruptcy attorney and explore your options for federal protection. The protection will even look back 90 days from filing and get back money taken by the collectors.
If your debt is with the government like the IRS or a State agency or for Child Support or taxes the rules will be different and you will need a local lawyer.
I do not practice in your state and you will need to consult with a local lawyer for additional protection under your state law.
I have pasted a link to the FDPCA to help you with your federal rights;