Electrical Help Please

If you have a big electric fan and have not upgraded your charging system, that could be an issue.
It also has MSD 6, a long battery cable to the trunk which draws extra power when cranking, and it has 2 electric fans, one for the coolant and one for the transmission. I think it has high compression but can't be for sure yet. Another reason it may be hard to start. I think a battery with more AH storage would be good as well as more CCA. Would a higher amp alternator help? Would buying a 125 or 140 amp alternator hurt anything by putting out too much?? I mean it could have a 60 amp alternator on there now for all I know. It's an Ultima 01-8152. I tried cross referencing it but couldn't find it. Looks like they sell Ultima alternators at O'Reilley's. I don't have one near me. Since the engine and trans didn't come in this car in 1968, it's kinda hard to look it up without a part number.