As usual, rules on this sort of thing will vary from country to country and from grant agency to agency.
However, all three options that you mention sound plausible to me. To go over them:
Decline the grant (...)
Sure. Nobody can fault you for declining a grant that pays so much below standard salaries. Honestly, unless I had no other options, this is likely what I would do. I am not sure I would call it "wasteful" to decline a grant that, honestly, sounds like a terrible option to begin with.
Convince the department to co-finance (...)
This is indeed not unheard of. Of course, whether you will be able to convince the department to do so largely depends on how much they want you to be there, what their regulations are, and if they have money to spare. I have seen this sort of co-financing mostly in cases where the department and the applicant were already in longer contact, and the public grant was mostly acquired as a way to make a move that was happening anyway cheaper for the department (that is, it was planned that the candidate joins them anyway, but now a part is paid via an external grant). If the department had no intentions to hire you without the grant it becomes substantially less likely that they will be willing or able to chip in.
(...) obtain another grant (...)
This sounds like another plausible option, but check the regulations of both grant agencies. In many cases, full-time personal grants are exclusive - that is, you can have only one at a time, even if the stipend is very low. However, it may still be an option to apply not for a second personal grant, but for a regular research project that allows you to pay a salary supplement for yourself. Whether this is possible again depends on the grant agency. For instance, the SNF in Switzerland as a rule never allows to pay any money to yourself as part of a regular research project. The FWF in Austria, on the other hand, is perfectly fine with this as long as the rules of the host institution (regarding, for instance, maximum employment), are followed. That being said, with this option you should probably expect to live off the 60% stipend for a while, as the application procedure for grants tends to take a while.