An exact answer would require a rather specific and mathematical formulation of the multiverse in consideration.
As a simple approximating example, suppose we have a countably infinite number of (observable) universes of the same mass $M$. Suppose the dimension of the full multiverse is one higher than each individual universe, and suppose the universes are all separated by the same minimum distance $epsilon>0$ from each other. In a 2-D picture, this would just look like a bunch of parallel lines all separated by the same distance.
Pick your home universe and put an observer. Another universe of distance $nepsilon$ away (meaning they're $n$ universes up or down from you in the 2-D picture) exerts a gravitational force on the observer in its direction approximately proportional to $displaystyle{frac{M}{n^2epsilon^2}}.$ With the right units, we can just say "approximately".
The maximum gravitational force occurs when the observer is at the bottom (or top) of the picture, and all over universes are above it (or below): universes on each side will pull in opposing directions and so lead to cancellations. So the net gravitational force from the other universes (in the right units) is at most
$$sum_{n=1}^infty frac{M}{n^2epsilon^2} = frac{M}{epsilon^2}sum_{n=1}^infty frac{1}{n^2} = frac{pi^2 M}{6epsilon^2}<infty.$$
If the observer was "in the middle"—infinitely many universes above and below, with the distribution identical in either direction— the net gravitational force from the other universes is exactly 0.
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