Add a tank and pump to tankless coil?

Is it feasible to add a storage tank and pump to an existing tankless coil that can't produce hot water fast enough? I am trying to get the most mileage out of my old boiler before I replace everything.

Rather than adding a crummy tank to the coil, buy a real indirect-fired tank with it's own internal heat exchanger and run it as a separate zone. The indirect will typically last as long or longer than a new boiler, and with bigger heat exchanger can use the full output of the boiler for "endless hot water". When it comes time to buy a new boiler moving the indirect over to the new boiler will be no more complicated than any other heating zone. Also, if your old boiler is cold-start tolerant (almost all gas fired boilers are, some oil-fired boilers aren't), with an indirect you don't have to keep the boiler hot all summer just for hot water with an indirect, doubling it's water-heating efficiency.