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Making no assumptions . . .
It is possible to put two batteries together in parallel, but if their capacities are different, one will tend to charge the other, resulting in net loss of power.
You could use some diodes to ensure that current only flows out of the battery packs, and then parallel them *after* the diodes. I did this in a ham radio config (I'm VY2CRV, btw) - I have an old Icom IC751, which has its RAM backed up by a lithium cell. Problem is, if you disconnect the existing cell, the RAM goes dead, and the radio is useless until you build a programmer for the thing. Not fun.
Solution? Well, looking at the module with the battery, it became obvious that they were using a diode setup to prevent the lithium battery from receiving charge from the operating circuit when the radio was one (which would kill the lithium cell, if not cause it to overheat.)
Solution? My good friend VY2OX (Lowell) designed a small board with two battery clips on it, each isolated by diodes. Now, when the batteries go dicky (in 20 years, mind you!) I can pop them out one at a time and replace them without the radio going poof.
If the radio lives that long . . .
So . . . you could do the same, with higher current diodes, and then remove the packs for charging, since the diodes would block the charging.
Just an idea.
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